A Captain's Log is a logbook or an entry therein where the captain of a vessel records the events of the day. Everything of note is usually recorded, such as changes in destination and arrival or departure times.
For Star Trek fans, it is a voice-over from the captain of the USS Enterprise informing the audience what is happening or where the ship is heading at the start of an episode. This allows us to get involved with the story without a lot of extra time spent acting it out.
For those in elementary school, it can also be a joke about a turd left behind by the captain of a vessel. Most likely used by Wesley Crusher.
Iron Noder 2017