If you’re in a situation where having or being around a certain aspect means your character’s life is more dramatic or complicated, anyone can compel the aspect. You can even compel it on yourself—that’s called a self-compel. Compels are the most common way for players to earn more fate points.
There are two types of compels.
Decision compels: This sort of compel suggests the answer to a decision your character has to make. If your character is Princess of Alaria, for example, you may need to stay to lead the defense of the Royal Alarian Castle rather than fleeing to safety. Or if you have a Defiant Streak a Mile Wide, maybe you can’t help but mouth off to the Dean of Discipline when he questions you.
Event compels: Other times a compel reflects something happening that makes life more complicated for you. If you have Strange Luck, of course that spell you’re working on in class accidentally turns the dour Potions Master’s hair orange. If you Owe Don Valdeon a Favor, then Don Valdeon shows up and demands that you perform a service for him just when it’s least convenient.
In any case, when an aspect is compelled against you, the person compelling it offers you a fate point and suggests that the aspect has a certain effect—that you’ll make a certain decision or that a particular event will occur. You can discuss it back and forth, proposing tweaks or changes to the suggested compel. After a moment or two, you need to decide whether to accept the compel. If you agree, you take the fate point and your character makes the suggested decision or the event happens. If you refuse, you must pay a fate point from your own supply. Yes, this means that if you don’t have any fate points, you can’t refuse a compel!”
The compel system is meant to be that "Life has struck" mechanic of the game. That means that while a GM could compel a good decision, the RAI is that they're almost always to compel more complicated or "interesting" events and decisions. As such, a GM gets unlimited compels.
But this is why the players can also compel each other, and why they have the capability to refuse compels. Think of it as online shopping. You see something, you buy it, and then a bill or online subscription you forgot about comes due, and now you're in the hole. You coulda stopped yourself if you just remembered(by spending a fate point to resist), but you forgot(because you didn't have it, or your player chose to get the free fate point).
EDIT: I'm not sure how self-compels are supposed to work since the only person who gets an unlimited pool is the GM as I understand it. Players are supposed to spend points to compel each other, so I don't know if that means a self-compel is a way of cheating the system, or if it's just a "I compel myself out of your compel, so i don't lose a Fate point."