Aside from a paced run, "jog" has the alternate meaning of "nudge" or "lightly push". It might make more sense if you heard "nudge your memory".
Jog your memory. Where does that term originate from?
I assumed it was a pun on the word "run", with "run" turning something on or starting something rather than actual running
I believe it is akin to "shake up your thoughts till you remember".