Assuming that all computers used a signed 32-bit integer for storing date and time, at precisely 03:14:07 UTC on Tuesday, 19 January 2038, the 32-bit integer would look a little like this:
0111111 11111111 11111111 11111111
, at 03:14:08, the entire integer resets, and goes right back to what the computer regards as 1901.