Hi Soyeon, The usage of "The Mother Ship", usually refers to something that is crazy, someone who is crazy, or an idea or concept that is hard to believe. In the movie it is referring to the concept of reliving his day or being to travel back in time as too crazy to believe. I hope this helps you~

"Mothership" is usually a main carrier unit (usually on the sea or in space themed stories) where it serves as the main platform where all smaller ships will centre around (think of a aircraft carrier, where little planes land and refuel from). I can't find a suitable situation in daily speech, so just think of it as a one off description (I tend to see it more in space themed stories).

@Marc and Darryl: There is no time machine in the film. The main character and his father have a natural ability to travel back in time. They just go somewhere dark, clench their fists, while thinking of the moment they can go back to and they are there. The film is somewhere between Groundhog Day and the Butterfly Effect, but in the RomCom genre.

Can you give us some more context? A mother ship is a big ship providing facilities and supplies for a number of smaller ships. So my guess is that knowing he can travel in time he can supply other people with stuff. So the time machine is called mother ship as metaphor. But I am really guessing here.