The latest time that can be represented in Unix's signed 32-bit integer time format is 03:14:07 UTC on Tuesday, 19 January 2038 (231-1 = 2,147,483,647 seconds after 1 January 1970).
Times beyond that will wrap around and be stored internally as a negative number, which these systems will interpret as having occurred on 13 December 1901 rather than 19 January 2038. This is caused by integer overflow. The counter runs out of usable digit bits, flips the sign bit instead, and reports a maximally negative number (continuing to count up, toward positive infinity). Resulting erroneous calculations on such systems are likely to cause problems for users and other relying parties.