Anything promissory has to do with a promise or agreement. Little kids who say "You promised!" are very interested in promissory matters.
A promise is an agreement to do something, so anything promissory is related to a promise. A handshake is often a promissory gesture. Legally, a promissory note is an agreement to pay someone money. In court, lawyers might argue about whether a certain statement was promissory – that is, whether it was a promise that must be fulfilled. Whenever this word comes up, be sure to read the fine print.