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.

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.

Another way of saying "Oh, Hey there!"

As started on the freenode network channel #tyreus