The phrase is an intentionally misspelled "Oh hi" and is usually used as a title on cutesy pictures of animals like on lolcats.
The phrase is often followed by a short, badly spelled sentence as if the animal/subject in the picture is talking to the viewer.
O Hai may also refer to these types of cutsey animal images in general.
Picture of kitten in a stack of business reports.
"O Hai, i am bein yur nu secritary. Get me cofy."
A greeting that has its origins in what is arguably the worst movie of all time: The Room (2003). This phrase is said about fifty times in the movie by various actors to various other actors, and very often at random, inappropriate times.
Johnny: I did not hit her, it's not true! It's bullshit! I did not hit her! I did NOT!! O hai, Mark.