A Timing Push refers to a Terran player leapfrogging their Siege tanks while towards their opponent in order to take advantage of an opponents temporary weakness to an attack from taking an expansion, having their strategy lose effectiveness, etc...
There are a variety of different timing pushes Terran players typically employ.
There are a number of timing attacks for Terran. The earliest being, "fact/cc/fact" where the Terran player typically opens with a standard FD into expansion but instead of adding an ebay and playing defensivly the Terran player adds a second factory when the expansion CC is around 50% completed. The Terran player then moves to pressure the Protoss with 4tanks+8vultures and any leftover marines. This is a strong timing against 1gate expanding protoss but is hard countered by any early Reaver or DT openings.
The next is a 4fact push with only 1 addon. With this push the Terran should fast expand and then add 3 more quick factories while only producing tanks from one fact w/ addon. This push is designed to be very vulture heavy so tanks are extremely important to keep alive. If you lose even a single tank in the early game or in the field this push becomes much weaker. Typically the Terran moves out with around 6 tanks and rallies all 4 facts to the field for fast vulture reinforcements. The weaknesses with this build are 2gate powergoon openings where the protoss is very dragoon heavy and has fast observers.