originally, a "twitter fuck", meaning that you were fucked over by Twitter in some way, either by the site itself, or another person on Twitter. More recently, it's been used to say fuck (noun) in a "friendly" way.
Aaron: the boss just fired me!
Jenny: what the twick?!
To cancel or temporarily interrupt a service paid for without notice to the customer when the provider wants to reduce costs and hopes the disruption will go unnoticed. From the acronym for Time Warner Cable (TWC) and the term "trick".
I was watching that show online and at a critical point the feed TWiCked! Argh!