the idea came from the approximate time James Wilkes Booth shot Abraham Lincoln at Ford's theatre. Lincoln was despised for freeing the slaves and when the pocket watch became a familiar item to people after the turn of the 20th century, it was a reminder of this incident for "advertising" purposes from watch companies. The time was closer to 10:15pm, but aesthetically looked better at 10:10 (IMO the hour, minute, and second hands that advertisers use looks like aY10:10:32). 150+ years later, watch companies still advertise their watches with this time set on the watch.
tldr;
it is a reminder of Abe being shot