When you check things off, you check off whole themes. When you try and do something, you succeed unless your Mistaken stops you. So what's the point of Aspects?
Just wanted to say that, yeah, SeaWyrm is correct. Aspects determine when you're allowed to use a Theme in conflict. For instance, if you only had Starlight Sword as a Blessing, you could only use your Blessing theme when using the sword. If you also had The Black Hole Gem, you could use your Blessing theme when either your sword or the gem was being useful to you.
There is a side note, which is that Aspects can sometimes alter the rules of the game. This isn't really heavily indicated in the main Polaris book (I think that there are two aspects that have any extra rules to them) but it appears more in Thou Art But A Warrior and I used it a lot in The Wish We Wish To Night, the supplement about black hole knights.
You check off whole Themes, but the Aspects give those Themes form, meaning and relevance: When you want to exhaust a Theme, you have to ask the Moons, who judge whether the Theme applies to the current situation. They look at your Aspects to make this decision.
For instance, in an example from the book, the Moons allow a player to exhaust their Fate Theme because one of their Fate Aspects is a character central to the conflict they're in. If the player didn't have that Aspect, the Moons might have rejected the use of the Theme, or else required the player to exhaust an additional Theme.
Check out the section in the rulebook starting on page 73.
Aspects also differentiate your character from the other characters and establish important details about them.