Your character's aspects convey the most important things about your character. When you are in a situation that an aspect can reasonably influence, you may spend a Fate point to gain a bonus of some kind. Conversely, if an aspect can have a negative mechanical or narrative impact on a situation the GM will compel that aspect, giving you a Fate point for your trouble.
There is a lot of advice out there on how to create interesting aspects for your character so I'll not go too in depth there. I will only reiterate the one sentiment that is universal to all who offer advice. That is, the best aspects are those that are double edged, that can be both invoked for an advantage and compelled for a disadvantage. Those are the kinds of Aspects that keep the Fate points flowing. And that means a richer game experience and more fun for all.
Now that you have a solid character concept, you will want to come up with an aspect that describes your character in the most basic of terms. Your high concept will include things like your character's heritage, his/her occupation (read "class"), and it might be a good idea to throw in a word or two that describes the character's most fundamental personality trait. For instance, Gilthanas Kanan's high concept might be Passionate Qualinesti Prince. The choices made for your character's high concept can have a huge impact on what your character has permission to do.
The role you've chosen should inform your high concept since that's what grants him permission to do cool stuff. Example aspects for each role can be found in the Role section.
Your high concept should indicate which of the many people groups that inhabit the world your character hales from. The various heritages and the permissions they grant your character are discussed individually in the Heritage section.
No one wants to read a story about a character that is good at everything. Your character's trouble is what makes him or her interesting. What is your character's weakness? What is it that he or she finds most challenging? What complicates his or her life? A trouble represents something your character struggles with on a daily basis. Tanis's human side seems to almost always be at war with his elven side. This manifests in his conflicted feelings for Kitiara and Laurana. His trouble is Torn between his human and elven heritage.
While a character's high concept names a character's heritage, it doesn't emphasize what elements of that heritage they most identify with. Examples of possible heritage aspects are provided in the heritage section.
The best Dragonlance stories tend to have a group of close friends and family at their center. This is where you describe your relationship to another character or to the group as a whole. Again, write a short two or three sentence paragraph on the Character Worksheet describing your relationships within the group. Then use that to come up with an aspect.
This last aspect could be any number of things. You could also just leave it blank for now and fill it in when you are inspired by the progressing plot.
The simplest thing may be to just have this be another Companions aspect about a different player’s character. That is most common and possibly something that the GM will require if this is the start of your character’s story. There are, however, other interesting options for this slot.
It could be that you possess an item of unusual power that you want to be an important part of your character’s story and don't wish for it to be lost through the course of play. We see this in the fiction with Raistlin’s Staff of Magius and with Goldmoon’s Blue Crystal Staff. Just remember that this is an aspect. It can be compelled as well as invoked, so you should have a conversation with the GM about what impact the item has on the story and when it will be appropriate to invoke and compel it.
Another option is to have this aspect describe something truly unique about your character. Is she destined to restore the honor of the Knights of Solamnia? Does he have a horrible secret? Really anything that could play itself out over the course of the campaign will make a suitable Wild Card aspect.