It being a mostly data-base issue, most unix systems were not (directly) affected by the infamous "Y2K" bug. However they are susceptible to a similar issue. Virtually all "POSIX" systems - including most unix systems, as well as linux - keep track of the number of seconds since the "unix epoch" began on 00:00:00 GMT on January 1, 1970 in a 32-bit number. If you ask a unix system what time it is you'll get back a number like (brb..) "1583616379", which corresponds to "Sat 07 Mar 2020 01:26:19 PM PST".
Actually it is only a 31-bit number, with the 32nd bit indicating whether the other bits are to be interpreted as a negative or a positive number. Unfortunately this means that in only 18 years - at 03:14:08 GMT, January 19, 2038 to be precise - that 31-bit number will "overflow" into the 32nd bit and unix systems will start returning a negative number for the date. Obviously this will have various unintended and undesirable consequences.