You are a person from my past who I have not seen for a long time. Seeing you brought to my mind (like an explosion) a bunch of memories from that time in the past we shared.

Jose gives a great definition. There is really not any good translation that is also short. It's an idiomatic phrase, and that is frequently what happens with an idiomatic phrase, unfortunately.

You make me take a trip down memory lane. It might have different meaning though. "A blast from the past" is used when someone (or something) suddenly appears in front of you or come in your mind and remind you of an old memory or feeling. "Take a trip down memory lane" may be used when a thought or something that has just happened to you, makes you remember a memory that leads to another and another as the metaphor implies; as if you're walking down a lane.