Shipping (from the word "relationship", not to be confused with shipping in terms of delivery) is a concept in fandom, which concerns itself with certain romantic links between two (and sometimes more) characters. Shipping often come to the surface in fan fiction, while maybe a only story arc on the show itself.
In Futurama, the best example of shipping would be the Fry-Leela relationship, which begins early on and has its back and forth throughout the original run with Fry being the more one-sided counterpart in the relationship.
Shipping also takes form in other words, such the adjective "shippy", which could inform one about a concept of a "shippy episode". And sometimes the word "relationship" is simply shorted to "ship". Fans focus on the "shippy" aspects of a fandom are often called "shippers".