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).
After losing the queen for nothing, the game is essentially lost, so many players resign instead of wasting their time playing a lost position till the end. Others choose to play on, either hoping that you will blunder even worse or run out of time. People are free to choose.
Losing the queen is just one example; in general, people resign when they think the situation is hopeless.
When you lose your queen, it's a big loss. A lot of people resign because the queen is the best while other pieces need some strategic thinking. I am not saying the queen doesn't require strategy, it's just very easy to run out of situations if your Queen is in trouble, while with the bishop, for example, it is easy to be trapped if you have no idea what you're doing with it.
My suggestion to people who resign when they lose their queen I would generally keep my queen until mid game-late game when you've done developing, when you bring out your queen early, it can easily be disengaged by pieces like pawns and knights, so I save it.
People also resign because they don't have confidence they could win without it, and I feel the same without it. If your opponent takes your queen without losing a piece of their own, it's really tough to recover from that, because the queen can essentially move anywhere. So my suggestion is save your queen unless you need to bring it out! Because a weak pawn structure or development can be chewed apart the queen if nothing is safe guarding it. For example, it's late game and you have 2 stowaway pawns, your queen will tear them apart and give you a path for a 2nd queen
Overall, they just leave because they don't feel like they can win without their Queen, so they resign. After all, it is the best piece and it isn't restricted to a single move like the bishop, it can go everywhere. Just pay attention to your queen ;)