Shipping is from the word relationSHIP.
Basically, it's the belief that two people should be in a romantic relationship together. <3
Sometimes people will mass together the names of the two people in a ship, such as Connie and Jeff could be "Jennie".
OTP stands for One True Paring, and basically it's a ship that you feel is meant to be. (And yes, someone can have more than one OTP.

There you have it! Have fun shipping!