Reputation for being an informant. It is used both in police jargon and street slang. It is NOT an actual jacket (as in a garment), or being beaten up (though it may result in being beaten up.) Jacket comes from the "file jackets" that were used by the police prior to computerization of records.
The phrase has part of its origins in the police interrogation tactic of threatening criminals who will not cooperate. Often the only reason a perpetrator doesn't snitch is because he fears it will get to the street and put him in danger. Ironically police officers threaten to publicize or have correctional officers publicize that a perpetrator's "jacket" says they are an informant to get them to inform. Someone with a "snitch jacket" is often just a willing informant obviously.
Son they trying to send me up north with a snitch jacket for 16 months! People asking me dumb s#!t like, "Oh I thought that carried a minimum of 3 years served? How you get that?" That's the normal plea deal but they trying to spin it to population to get me to drop dime. Guess I gotta snitch!