Doubling as a famous quote, "Make my day" is urging someone else to provide an excuse for a violent confrontation, which will provide pleasure to the speaker. This may or may not be used as a bluff.
More broadly, if something makes your day, it has made the day a good one.
Example 1: "Sure, throw the first punch. Make my day. I'll enjoy hitting you back."
Example 2: "I just got a call from my Uncle Jack. I haven't heard from him in two years. It really made my day! I wish he'd call more often."