Recommended digital cameras?

I've been interested in photography for a while. I'm finally taking a photography class. The instructor said to get a camera with decent aperture and something else… I can't remember.
First, what exactly is DSLR? I know it's digital single lens reflex, but what is so special about it, and can you get interchangeable lens with them?
Also, what are compact system cameras? Those seem more expensive.
What about cameras with a flip out/around screen?
I also want burst mode.

It seems like a lot of questions, but I really want a decent one. Any suggestions?

The other thing he/she said was shutter control.

Here is a list of entry level DSLR cameras.
Sony Alpha SLT-A58 - $450, Canon T3 - $400, Nikon D3100 - $425, and Pentax K-500 - $470.

SLR means you can look through the same lens as what takes the photo. So you see what you're going to get.

DSLR's have to have interchangeable lenses. You should start with a kit lens and then figure out what lens you want next.

Compact system cameras can mean several things. Usually it refers to small interchangeable lens, mirrorless cameras. This article explains it in detail.
http://www.techradar.com/...ra-1031090

Flip screens and fully articulate screens are handy to have when videoing or shooting stills over the heads of a crowd or down at belt level to be at the same level as a child.

All of them have a burst mode.