To put it most simply, "pray" is to get in touch with the Immortals. Since the Immortals fulfill two roles, pray does to.

Option A) As you mentioned, OOCly contacting the Imms as the "People who oversee the game and fix brokenness, stop cheating"

Option B) Very powerful godly beings in the game. This is where you see people mostly pray when involved in religious aspects. As to which sort of player Immortals prefer to deal with...in my experience, I tend to see that Immortals *PREFER* the roleplay. Of course, PK ability can factor into that (Sometimes you've just got to accept if you're a lame, lazy dwarven warrior, you *PROBABLY* aren't going to be Ordasen's favorite person, in character). Many of my favorite Immortal interactions dealt with Immortal characters who DIDN'T like my character, but the person playing the Immortal did.

Hopefully that made sense, but to sum up, you were pretty much on the ball, and as long as you make an effort to roleplay, usually the Immortals will take an interest.