Now THAT is really helpful. Thanks, Yora.
So Compelling an Aspect is when they player takes over narration of external story or NPC elements, and Invoking an Aspect with they take over narration of internal character elements?
Yes, but also the GM is going to be compelling a player's aspects a lot.
But first let me answer your first question. Non-High Concept, non-Trouble Aspects are merely character traits that come up a lot. These are the things that you, the player, want to emphasize about your character, what you want to show up during play. These are double-sided coins, so that the player can use them to his advantage, but the GM can use them against the player when appropriate.
For instance, a character may have "Stubborn as a Mule" as an aspect. This does not define their character (so it's not a high concept), nor is it the real source of all their problems (so not a Trouble), but it's a trait that can also be a flaw. Now, Stubborn as a Mule basically means "I refuse to give up or back down" - so then you think when would that benefit a player, and when would it hamper a player?
The character could invoke this aspect when they are, for instance, being attacked psychically, and they are just too stubborn to be controlled. They could do it when they are losing or cornered, and need that last oomf - they just won't go down! They could use this when they are injured but need to flee.
The DM could use this to his advantage, however, by having an enemy compel this aspect if the enemy is trying to goad the PC into a fight. Or, perhaps the PCs are trying to sell some stolen goods. The group could get a reasonable price, and then the GM looks at the player and says, "But you're Stubborn as a Mule, don't you want a better deal?" He'll give the player a Fate Point if the guy keeps pushing after a reasonable deal, Or the player has to pay a fate point to take the offered cash. This could happen if the players are trying to surrender from a tougher foe, or the cops are trying to make the PCs leave an area. (I am reminded of Marty McFly and the word "Chicken" here.)
Many systems try to emulate the rules of the universe, simulate how the world works. FATE tries to emulate Fiction, and it's about simulating a cool story with big characters. In FATE, characters succeed at things because of WHO and WHAT they are (their Aspects); Batman has just the right gadget for the occasion because he "Has A Gadget For That", Superman can stop a train with his face because he just IS the "Man of Steel".
Once you figure out the aspects of a place, a character, etc, then you want to tag the hell out of them for your advantage. Now, remember that as a player, having your aspects compelled by the DM is a
good thing because it gives you more Fate points, and Fate points lets you tag aspects. So you want those Aspects that can be used against you. Sure, it makes things harder on your character, but that's where the fun lives - repercussions based on Who and What your character is, which makes a good story.