Episodic memory is defined as memory for a past, personal event, that involved recollection of the "who, what, when, where" and even "why" and "what it felt like" aspects of a past event in one's life. Some, including Tulving, have argued episodic memory is a form of mental time travel, with Tulving arguing that it also involves autonoetic consciousness, or the sense of reliving the event in one's mind. This idea has been highly controversial and strongly investigated in other species.
EM is often contrasted with semantic memory, which is memory that can be shared with many people, as it is memory of specific facts. This can include facts about events, of course, that do not include the personal aspects of episodic memories.
As an example, it is semantic memory to know that Sid Bream scored from second on a really close play at the plate to send the Braves to the World Series in 1992. It is episodic memory when I recall that my tennis coach jumped up onto the couch, which broke in half, when that happened, and that later that night I (I mean, a friend of mine) tried to ride a police horse, which already had a police officer on it*.
*to be fair, he was directing traffic with a giant tomahawk, so it was one of those all-bets-are-off nights. And, by he, I mean the police office, not the horse. That would have really been something.