This is a huge topic, so I must apologize in advance for the novel you're about to read. However, looks like MarkBarbieri above already summarized everything I'm about to say into 4 succinct paragraphs.
There are several things that set DSLR cameras apart from point-and-shoot / bridge cameras.
Image quality
First and foremost, the ultimate feature that sets DSLR cameras apart is their much-better image quality! I've owned several point-and-shoot and bridge cameras in the past. However, once I bought my DSLR and saw the photos it took, I made a vow to go back to all the vacation places I'd been to over the past 10 years and re-do all those photos with a DSLR! Yes, the image quality is THAT good!
I'm not a photography pro or expert, but here's what I saw in terms of image quality. DSLR pictures are lots sharper and they have a lot less noise / grain, especially for low-light photos.
There are several reasons for better image quality. The image sensor in your point-and-shoot / bridge camera is actually very very small, perhaps as small as 5.5 x 4 mm (that's millimeters!!!). On the other hand, most entry-level DSLRs have at least a sensor about 23.5 x 16 mm. If you calculate that out, you'll see that the DSLR sensor size is about
17x larger than a point-and-shoot sensor. A larger sensor is a good thing because it allows your camera to gather more light for your photo.
Here's a photo from Groucho (another member on these boards) that illustrates this point:
(the 2 smallest photos would be from point-and-shoot / bridge cameras. The 2 largest photos would be typical DSLRs. The "4/3rd" size comes from a smaller, more compact DSLR only made by Olympus)
DSLRs are also very good at
night & low-light photography. This is partially because of the larger sensor, but also because of larger aperture lenses that are available to you. Your Konica Minolta Dimage Z10 had a maximum aperture of f/3.2. If/When you buy your first DSLR, for an additional $100 you can also buy a 50mm f/1.8 lens. With aperture numbers,
the smaller the f-number, the larger the aperture. A lens with f/1.8 will let about 3x more light into your camera vs f/3.2. (And if you have more $$$, a lens with f/1.4 will let in 5x more light...).
Photography is all about the light.
Larger-aperture lenses are what you'll need for low-light and night photography. Larger apertures allow you to use faster shutter speeds for the same photo / same exposure. This means that sometimes, you can even hand-hold your DSLR camera to get decent night photos or fireworks photos.
Those numbers that I calculated above (3x more light, 5x more light...) means that you can potentially use a shutter speed that's 3x faster (or 5x faster) compared to your Konica camera, and achieve the same exposure / same photo.
If your child / friend is in theater or performing a show, DSLRs are also very good for this low-light situation, given the right camera settings and lens.
Faster shutter
When people buy their first DSLR, the very first thing they notice is that a photo is taken
immediately after they press the shutter button, not 1/2 second later, not 1 second later. The shutter lag time is virtually instantaneous on DSLRs.
This may not be a big deal for taking photos of stationary eBay items. But folks with kids love the faster shutter speed! Your baby makes a cute face, and your DSLR can
instantly capture that face. Your child jumps into the swimming pool, and you can capture your child mid-air. Try taking the same photo with your point-and-shoot--your kid will already be out of the pool & drying off by the time your camera
finally decides to take the photo.
Sports photographers and wedding photographers depend on this faster shutter feature. Parents whose kids are in sports depend on the faster shutter speeds, too.
Versatility
With DSLRs, you can use different lenses for different situations. Each photographic situation is unique, so you probably shouldn't depend on a one-size-fits-all lens to take optimal pictures of everything. That's why switching lenses for different situations can be a good thing.
If you take macro photos, you'll get the best results by using a macro lens. If you're attending a wedding and want to take photos with your DSLR, take a lens with a large aperture (small f-number) so you can take photos without bothering the ceremony with a distracting flash. If your child is in sports, but you're stuck in the stands, you'll want a telephoto zoom lens (which is also good for Kilimanjaro Safaris at Animal Kingdom). At the Grand Canyon, you'll probably want a wide-angle lens.
Different photographic situations call for different lenses.
You mentioned that you were doing product photography for your eBay listings. I'm sure your eBay customers probably don't care about camera lighting. However, with a DSLR, you can invest in an
external flash that attaches to your camera and learn to soften the light from the flash. You can also use a technique called "bounce flash" to give some soft, directional light, too. All this will give your eBay product a more even and pleasing lighting, setting your product apart from other eBay sellers. (dealing with crazy eBay customers, on the other hand, is a different story altogether...)
But an external flash can also do wonders to improve your everyday photography, too...even in daylight!
A lot of folks who buy their first DSLR already see an immediate difference in their photos, even on the "Auto" setting. They see that their DSLR has a much faster shutter response time (less shutter lag) and their photos appear sharper.
However, to take FULL advantage of your DSLR, you've got to take some time to learn:
- the principles / basics of photography (ie. shutter speed, aperture, ISO, etc)
- topics specific to *digital* photography (ie. RAW vs JPEG, histograms, etc), and
- digital post-processing of your photos (ie. how to use Photoshop Elements / Lightroom / Aperture to develop your photos and make them better)
These are all topics that are covered in any "Intro to Digital Photography" book that you'll find at your local bookstore. They're also covered on hundreds of different Web sites that teach Intro to Digital Photography. These questions also come up very frequently on this message board, too.
There are several disadvantages of DSLRs.
Heavy / not as portable
You can't just slip a DSLR into your pocket / purse and walk around Walt Disney World. You (or your spouse / BF / GF / BFF / whoever) will actually be
carrying it with you all around town or all around the parks. My neck and shoulder muscles have gotten a real work-out over the past several years.
You'll also need to invest in a camera bag or camera backpack for your DSLR camera, lenses, and accessories...making it a little (a lot) bulkier for travel.
People think you know a lot more about photography than you really do
I was talking to a guy once who was carrying around his brand new Nikon DSLR and asking me tons of questions about his camera, and I was happy to help him out. I tried to tell him the basics of about shutter speed, aperture, exposure, but all that info seemed to go way over his head.
I gave him some tips on how to focus on a subject by pressing the shutter half-way down. He had a puzzled look on his face, "What's a shutter?" I explained it to him, and he said "Oh, THAT thing? I just call it 'THE BUTTON'."
Later on, he tells me that a bunch of his friends & family members have already asked him to do wedding photography for them! He was in a panic because he knew that his photography skills weren't quite there yet, but his friends & family thought "big camera = good photographer".
Other new DSLR photographers, though, don't know their own limitations, and they really DO go into wedding photography, charge super-super-cheap prices, attract couples with small budget for photography, and produce horrible wedding photos...ultimately to the disappointment of bride & groom.

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Spending
Once you spend the first several hundred $$$ on your first DSLR, don't think that the spending stops right there! You will quickly learn that you want / need additional DSLR lenses and accessories. Certain lenses are better for different types of photography. Your budgeted spending for photography will very quickly balloon into the thousands of $$$$$ over several years (hopefully, not over several months).
Ultimately, I'd say that if you're already getting and are satisfied with the pictures that you need with your current camera (or with another Konica camera), then you probably should not spend the hundreds or
thousands of dollars on a DSLR and its associated lenses & accessories.
As an analogy, my modest 10-year-old Toyota Corolla gets me from home to work and back without any problems, and I can run errands and get around town nicely. However, I see that some people in my neighborhood have upgraded their cars to the latest truck / mini-van / sports car / SUV. Some folks have a need for a pick-up truck / mini-van / sports car / SUV cuz it makes them more productive. But I find that my trusty Corolla does exactly the tasks I need.
However, if you feel like your photography is somehow being hindered by your current camera, then perhaps it is time to upgrade to a DSLR.
Sorry for the super-duper-long post. This "DSLR vs. non-DSLR cameras" is actually a HUGE topic, and I'm sure I'm missing a ton of information, so please read what other folks have to say, too. Hope that helps, and let us know what camera you end up buying!
(and if you buy a DSLR, buy a Canon!

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