What do we know about Aiden:

Backstory:
Aiden Burn was fired by Mac Taylor for tampering with evidence in the case of D.J. Pratt, a rapist she is trying to nail. She is later killed by D.J. Pratt.

Relationships:

Danny Messer: They may have had an unofficial romance after she was fired, but while she worked for Mac, they had a close friendship. They occasionally flirted, but that's about it as far as we know.

Regina Bowen: Aiden formed a close friendship with multiple rape victim Regina. It was Aiden's friendship with Regina and her angry emotions toward rapist DJ Pratt that got her fired in the end.

Don Flack: Throughout season 1, it looks like Aiden and Flack have a good friendship relation. In some episodes when they work together, they seem like a good team (as well as with Danny) and they joke around a lot.

Defining Cases (or Episodes):

Secrets:

Trivia: She and Danny may have started unofficially going out after she was fired.
Her murder made Lindsay feel a bit uncomfortable seeing as how Aiden was close to everyone, especially Danny.

It is revealed that Aiden worked for Mac for more than six years, you can hear Mac say in the episode "Heroes" how a "young detective" linked a murderer to a case.

Quotes:

"He died because of his wife, and she was the only one who loved him."