Transpire is a fancy way of saying "happen." You might go to a fortune teller to find out what will transpire in the future.
Originally used to express when information became known or came to light, many purists will tell you that's really the best way to use transpire. It can also mean releasing vapor into the air, like when a plant transpires water through its leaves on a hot day. Note: you'll usually encounter this word in its past tense: for example, "We had to watch the replay to figure out what had transpired."