Most POSIX puters keep track of time by measuring the seconds, not including leapseconds, since the Epoch.
Since the Epoch occurred at midnight, December 31, 1969, it was generally easier for 20th-century programmers if dates were expressed as an offset from 1900, rather than 1970.
This isn't universal, of course. MS-DOS expressed years as an offset from 1970.
Hang onto your hat, because it's all going to need changed in a few years, anyway. The variable used to hold the number of seconds is going to run out of bits very soon now (in the 2030s?) and we're going to have a new Y2Kish problem.
I expect that within a decade, there will be new POSIX date functions that are based on 4-year dates, so that with any luck, we'll have discarded any old software well in advance, but there's probably still going to be 1960s-era COBOL code around.... (That, of course, predates POSIX, but the Y2K patches wouldn't....)