As others have said, RAW saves a lot more data in the file, and allows you to do more with the photo if you need to make adjustments. The one down side of RAW format, though, is that it is just that... raw data.
When you're shooting with your camera's "L" format to get a large, or high quality, JPEG file, the camera is doing a lot of work. It's applying settings to enhance the photo before it saves it to disk. It applies white balance, noise reduction, and other enhancements. The final product of these changes is what's saved to the file.
In RAW mode, you need to "develop" every photo. The camera saves exactly what it saw without applying any edits. Straight out of camera, the photos probably won't look as good as your current "L" photos do. Using a software package like Lightroom gives you the ability to develop the photos to your own creative tastes, and gives you much more flexibility for a better final product than might have been possible in JPEG mode. It is possible to create presets in Lightroom that would allow you to automate some of the developing during import, but know up front that there is a certain amount of post-processing time required with RAW that isn't necessarily required with JPEG.
Adobe offers a free 30-day trial of Lightroom on their web site. It's a fully-functional version of the software, and is available for download. Your camera may also have come with a free software package for RAW processing. For example, Canon DSLRs come with Digital Photo Professional.
One last consideration if you're thinking about RAW file format is the fact that the files are in a format that's proprietary to your camera manufacturer. They need to be converted to an open format (such as JPEG, GIF, PNG, etc) before they can be used in many software applications or shared to social media. To view them on your desktop, you would also need to install your manufacturer's CODEC on your computer, which allows Windows to read and display the files in explorer.
Lightroom is great for developing, but is also a wonderful organizational tool. I've been using it for about a year and a half, and would be absolutely lost without it now. I also have Photoshop CS6, which I only use if I need to do some serious editing (such as cloning something out of the photo, applying layers, etc.) Everything else I process directly in Lightroom.
Before spending the money to purchase Lightroom version 4, take into consideration Adobe's recent announcement that all future versions of their creative suite software will be available by subscription only. I'm not sure if this applies to Lightroom. If it does, it would mean that unless you're willing to purchase a monthly subscription, you'd be stuck at version 4 forever.
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