Follow suit.... is what you do in some card games. If someone puts down a diamond (a card! not a real ONE!) you must follow suit and put down a diamond too.
In a pack of cards there are 4 suits (diamonds, hearts, clubs and spades)
You must follow THE suit in play.
So we now have the expression 'to follow suit.' It is in general usage for all sort of situations where you must follow someone's lead/do the same thing.
For example, if someone at the end of a play STANDS UP to applaud then other people might STAND UP TOO. They follow suit. Soon everybody is standing and applauding. It must have been a very good play!