I'll elaborate on my good friend freakdave

SDLx is a wrapper for DirectX.
This means you can do some low-level graphics, like blitting bitmaps, for example if you were writing a 2D version of Pong. It also allows you to play sounds using the SDL API's functions instead of all DirectX, which can be confusing for the younger of the coders.
SDL is widely used, it's multi-platform, so you can write a program for Linux, and with a few tweak, it'll work with SDLx too.
does that make sense?
It basically wraps the DirectX API into a whole new set of classes.
For instance, SDL_Init( SDL_INIT_VIDEO ) will initialize the DirectX window.
Instead of you writing possibly several lines of code, you need one.
It basically simplifies coding, but it doesnt offer the full power of DirectX.
As far as i'm aware, you can only really do 2D Stuff with SDLx.
Yes, of course you can develop games with it.
http://www.libsdl.org (official site)
http://sdldoc.csn.ul.ie (the documentation)
http://jnrdev.weed-crew.net (some tutorials)
http://www.lantus-x.com/forum (just check the SDLx forum)
http://andrew.textux.com/Articles.html (another tutorial)
Right from the horses mouth.
Thanks lantus!