What is the "Run Command" dialogue?

Question

1. What is the "Run Command" dialogue that comes up when you press
   Alt+F2?

2. Is it the same thing or in someway related to the menu that comes up when you press Alt from inside a application (like Firefox for example)?

3. What kinds of commands can you run inside it?

4. How similar is it to the command line terminal?

I use Ubuntu 14.04.