Mina:
"OTP" indeed means "One True Pairing". It's used to describe your favorite combination of characters in a fandom. It's usually used via putting the names or name abbreviations together, sometimes with the use of a + , / , or X . (For example my OTP for Naruto is ShikaTema , = Shikamaru + Temari.) OTP is also just used to denote a pair of people that are the "perfect partner" for each other in the opinion of the person marking them as their OTP. The name that comes first in the pairing is usually the "seme", aka the "dominant" partner in the relationship, though this isn't too commonly followed anymore.
"Shipping", or "the ship", comes from the word "relationship". It describes the action of being... "enraptured" by the prospect of a pairing, and actively pushing the said OTP onto other people. Fans create new settings, stories, doujinshi, fanart, and are generally obnoxious with their excitement over the possible romantic involvement of the characters they "ship together".
Shipping/OTP's have generally a lot, little, or nothing at all to do with "canon", aka the official set in stone situation the two characters/people originate from. For example the canon in Gyapun's first OTP is virtually nonexistent, since Mina isn't gay. But that doesn't stop the shippers. (Duh, fans be crazy, yo.)
I hope I made sense here X_x.