For engines the time between overhauls is generally a function of the complexity of the engine and how it is employed. Piston-based engines are much more complex than their turbine-powered cousins, and generally have TBOs on the order of 1,200 to 2,000 hours of running time. They tend toward the lower number if they are new designs, or include boosting options like a turbocharger. In comparison, jet engines and turboprops often have TBOs on the order of 3,000 to 5,000 hours.
Since the overhaul process requires the engine to be taken apart, it is typically an expensive process. The value of a used engine decreases if it is close to requiring an overhaul, so used engines (and aircraft) typically list their time since overhaul or TSOH.
The TBO is a time 'recommended' by the manufacturer and depending upon what rules the aircraft operates under, overhauling the engine at this time is not necessarily mandatory. For aircraft used for non-commercial purposes overhauls are not mandatory, but highly recommended. Likewise, overhaul at the recommended TBO doesn't guarantee that the engine will last that long.