Close the doors to the room you're in. I hope it's a very nice room, with many things to keep you occupied and things to keep you occupied. Take a broom and knock on the ceiling. Push on the closed door. That's a p&s like the Nikon Coolpix L120. You have a very good compact camera with many features.

Now, open the doors and peel off the ceiling. That's a DSLR like the Nikon D3100 or D3200. You now have removed the limits of what you can experience. Even though the D3100 is an entry-level DSLR, it's a gateway to the vast Nikon ecosystem, and a portal to everything that photography could be in your imagination.

Differences?

Larger sensor for greater image quality.

Interchangeable lenses so you can choose exactly the right tool for your creative vision.

Fully adjustable modes so you can make the decisions, and not just rely on automation.

A system you can grow with and into.

I have an excellent Canon SX compact digital that I picked up for "those times" when I can't bring my Nikon DSLR. Guess what? 98% of the time the Canon is left at home, because I know I can capture the images I want with the DSLR and won't be saying to myself afterwards, "If only I had..."