A threat. Used to indicate the speaker's intent to exact serious retribution from the owner of said ass. The literal threat is that the speaker will take ownership of the ass as their property and will freely penetrate the anus at their discretion, either for sexual pleasure, to inflict pain, or both. However, this literal act is rarely the intended form of punishment the speaker wishes to mete out. Usually, the speaker wishes to convey they will exert the full extent of their authority over the other person to assert dominance over them. Loss of bodily autonomy illustrates submission.
Commonly used as an ultimatum; e.g., "if you crash my car, your ass is mine."
Typically, this is used only amongst males where the threat of anal rape is playful banter with a homoerotic undercurrent. If used against the opposite sex, the threat of sexual violence carries a more severe tone and would be highly inappropriate.
Related phrases:
You selling your ass, boy?
I own your ass.
The game is over, your ass is mine! (Ferris Bueller's Day Off)
If you drop the ball again, your ass is mine. (my sixth grade football coach)