Why do players resign after accidentally giving their opponent a free queen? Whenever I verse players in Live Chess (30 minutes) on Chess.com, sometimes I am able to threaten their queen because they brought it out too early in the game. In the opening/beginning to midgame, if I threatened their queen with a simple move, and they forgot to move it away or block the attack, and I take their queen on the next move, they resign. Why?
Material (i.e. basically who has more and better pieces) is a very important factor in the objective evaluation of a chess position. The queen is the strongest piece on the board, roughly equal to two rooks or three minor pieces (knights or bishops).

If you really drop a queen in an otherwise equal position you are going to lose 99.9% of the time. Rarely you have situations where you have compensation for being a full queen down, like for instance you have a very strong mating attack or perhaps the queen is bound to protecting a pawn from queening, etc.

If there is no such compensation it is very reasonable to resign. There is not much point (and not much fun) playing a queen down. In fact most slightly advanced players would resign being a minor piece (knight or bishop) down in otherwise normal position (no attack, etc going on).