Billy Costigan's uncle Jackie is mentioned in The Departed with Queenan and Dignam, then again during Sullivan's briefing scene. How was he important to Frank Costello's crew?
It's never mentioned what his exact role was. All we know is that he was working for Costello as a probably not too important but loyal mobster.
We learn that he probably was no stranger to violence when Costello approaches Billy:
Costello [Talking about Billies father] No. He kept his own counsel. He never wanted money. You can't do anything with a man like that. You're Uncle Jackie - he also would kill my entire fucking family if he saw me here with you. And I think about this.
So Costello is implying that Jackie was a different man than his brother William Costigan. He spoke his mind and could be motivated with money.
A later conversation makes it clear that Jackie had earned his trust in the crew:
Frank Costello: [talking about Costigan] Do you trust him?
Mr. French: Well these days, who's reliable?
Frank Costello: His uncle Jackie was. Yeah, you can't trust a guy acts like he's got nothing to lose.
He got killed when Billy was still young:
Ellerby: By organized crime in the city, you know who we mean - that's Jackie Costigan, that's an old picture. Jackie met his demise. Last known photograph.
(all quotes taken from IMDB)
That is pretty much all I could find regarding Jackie. He did not play a big role in the movie, the main purpose of the character was to give Billy Costigan a family connection to the mob. He is the reason Costello approached and recruited him, because he knew and trusted Jackie and saw that potential in Jackie's nephew as well.