Edmond Gettier was a 20th century philosopher, best known for his challenge to the idea that knowledge was "justified true belief", which was a long held belief, possibly as long as 2000 years, going back to Plato, and probably Socrates. "Knowledge" was thought to be a special kind of belief that was both true (you can't know things that are false) and justified (you can't simply have guessed the truth). Gettier came up with situations where you both believed something that was true, and you had strong justification for that belief, but it still didn't seem like you "knew" it, because the reason for the justification was disjointed from the reason for why it was true. These scenarios because known as "Gettier cases" or "Gettier problems".
David Lewis was a 20th century philosophy known for his work on counterfactuals. A counterfactual is a statement about what would happen if things weren't as they are in a certain way. For example, you might say, "Al Gore would have been president if he had won Florida". David Lewis realized that these kinds of statements were extremely problematic in the way that we normally think about truth, because something is true if it corresponds to a thing that exists in the world. In other words, something that exists in reality makes it true (if I say a cup is red colored, it is true because of a property of existence - the redness of the cup), but for a counterfactual statement you can't point to anything existing that makes it true, because it is about things as they don't exist. David Lewis came up with the rather bizarre solution that counterfactuals must point to possible worlds, which exist not only in theory, but in fact. It is the possible worlds which guaranteed the truth condition about statements of what could have been, to rescue their coherence.