Yesterday, time on Earth had a leap second. The planet's computer systems survived unscathed, thanks to months of careful preparation by engineers. But here's a concise explanation of why, left to their own devices, a bunch of very expensive computers could've thrown a hissy fit.
YouTuber Tom Scott explains the system, called Unix time, that computers use to track the passing of seconds. It counts the passing of time using one number, the number of seconds elapsed since midnight, January 1, 1970, in Greenwich Mean Time. The bigger the number (it was 1435803530 while writing this post) the later it is. But if that number occurs twice, as a leap second could cause it to, that can cause all sorts of glitches in computer systems.
The solutions used varied from institution to institution: Google broke the leap second up into 'smears' and distributed them across the entire day, thereby avoiding a duplicated Unix time; stock exchanges, subject to the demands of high-frequency trading, simply opted to shut down early. Either way, it seems that it all worked -- midnight came and went without any computer explosions.