Why are you tired of your point and shoot? What do you currently use?
What's the biggest complaint with your current camera?
Specifically, what types of pictures do you want to take? Family portraits where family is posed against a backdrop of some sort? Action shots of kids in sports?
You may be ready for a bridge camera or you may want to move up to a dslr as the previous poster asked.
There is a big difference between "I want to be a better photographer" and "I want a camera that takes better pictures." That's why people ask.
If you know nothing about photography, but do wish to, the best place to learn is to go to your library and pick out a few photography books. Digital photography for dummies would be good too. Read them and then ask yourself the questions again.
Do you want to be a better photographer?
If so, and your current camera allows more manual control, practice with that to see the effects of what you learned from reading at the library.
Then, you can decide if your new skills warrant a good upgrade to a bridge camera or a lifelong passion (and potentially big bucks) for a dslr.