A nickname for reddit. It is taking the piss out of the cancerous "rage comic" meme that describe everything with 'le'. Coined (like most things) on 4chan, the arch-rival of reddit.
When an event or individual is so legit, that the single term "legit" is too commonplace to describe it. Multiple legitly's can be included for added effect.
Man #1: Dude, my wife just gave birth to a son!
Man #2: Nice! What did you guys name him?
Man #1: Perry.
Man #2: THAT'S LEGITLY LEGIT
a shortened form of the word "legitimate". however, this term is nowhere near the real meaning of "legitimate", since it is commonly used to describe things as cool or extremely awesome.