A Great Slide is when your bird slides down a hill (via: pressing and holding on the screen, and letting go) perfectly without bouncing or anything else that counts as an error.
How to get a Great Slide:[]
You can get a Great Slide by making no errors whilst sliding down a hill. It can be rather tricky when you have just started the game, but it gets easier when practice. If you get 3 Great Slides in a row, you can get yourself into Fever Mode.