What we remember is not necessarily what really happened in an event:
False Memories: When Your Brain Makes Stuff Up | TIME.com
Human memory isn't like permanent data storage on an electronic device. Short term memories are transferred to long term memory (that appears to be the primary function of dreaming). But once it's there it can be rewritten and revised. Here's an example of an experiment done with mice in which researchers implanted false memories:
False Memories in Mice | MIT Technology Review
This is obviously a problem that affects eyewitness testimony in courts:
https://en.wikipedia.org/wiki/Eyewitness_identification
And from the following article: "One thing to emphasize - a false eyewitness identification does NOT mean that the witness was lying. The witness is convinced that the identification is correct. Psychological research confirms this. ... What emerges from all this is the idea that a witness' degree of certainty does not necessarily have any connection to the actual truth of the identification. It is possible to be completely convinced, quite certain, and dead wrong! This principle applies in many other areas as well."
http://www.physics.smu.edu/pseudo/Eyewitness/
Which isn't to say everything we remember is a false memory, but if we remember something we later find out happened differently, it's likely a case of false memory.