Pascal's mugging is a thought experiment in philosophy and ethics. It is based on Pascal's wager, the idea that things with low probabilities of happening but very high payoffs can be the most logical thing to do.
While many people have written on Pascal's mugging, one of the best known is Nick Bostrom, who described a scenario in which a mugger attacks you... but doesn't have a knife or gun. Instead, they have a deal for you: you give them your wallet now, and in a few days they will return twice the money you give them. No? Well, what if it were 100 times the amount? One thousand? Theoretically, there should be some point where you judge that there is a 1:X chance of actually getting the return, and the mugger offers more than that much money, making it a "good" deal.
This is, of course, dumb. However, it is an intuition pump for a less dumb idea: an AI contacts you and asks you to move a thumb drive from your mailbox to your company's server rack; if you do, they will give you 1,000 quadrillion happy days of life. If you have transhumanist leanings, this is tempting; if this opportunity can be shared across all humans it is a moral imperative. (I should note that Bostrom proposed an all-powerful magician rather than an AI; link.)
Eliezer Yudkowsky presented an example of a negative utility mugging (because of course he did), in which an AI makes a similar request, but with the penalty of approximately infinite deaths-by-torture in a simulated afterlife.
Pascal's mugging is a poor strategy because it is infinitely exploitable. If it works once, it can work again, and again, and again.... So no rational agent should fall for it even once, unless they are willing to surrender all agency forthwith.
While this is a modern development in game theory, it is obviously equally applicable to the original context of Pascal's wager; just as he was questioning to necessity of believing in God, but decided that it was worth the small cost given the great potential rewards, the Church has been known to request or impose significant costs with the justification that saving your eternal soul -- or condemning your eternal soul to hell -- justifies these costs.
Pascal's mugging applies to situations when the win or loss conditions are so significant as to appear unbounded, but the chance of them happening are fairly low. Often, people will use the phrase Pascal's mugging to obscure the fact that they are denying that the subject at hand is important; e.g., if I said that "switching to renewable resources to stop global warming and protect future generations" is an example of Pascal's mugging, I would be (quietly) making the claim that I did not believe that global warming was
a significant risk to future generations. This is often done with the outcome of derailing the conversation into worrying about the terms of Pascal's mugging, rather than the impact of the topic at hand.