Pick any moment in time. Subtract midnight UTC on January 1, 1970. The number of seconds you get is the Unix timestamp.
It's how nearly every operating system, database, and programming language stores time internally. Time zones are layered on top for display only.
Modern timestamps usually use milliseconds (13 digits) instead of seconds (10 digits). And in 2038, signed 32-bit timestamps overflow, the 'Year 2038 problem'. 64-bit timestamps fix it.