What is the definition of a tolerance on a dimension typically found on technical drawings?

Tolerance allows manufacturers to accept details provided by engineers,

Tolerance is an acceptable amount of dimensional variation that still allows a part to perform as designed

Tolerance allows people to accept differing points of view.

Tolerance allows engineers to be able to accept the work created by manufacturers.

Tolerance is the acceptable amount of dimensional variation that still allows a part to perform as designed.

Any process will have variation and depending on the severity of the function some tolerance will be very small. For example the sheet metal thickness on portion of a space shuttle will have a much tighter tolerance than the thickness of a piece of lumber to build a house. Tighter tolerance of processes typically are related to more process control (e.g. money) thus designs should be fully vetted with process team before placing on a drawing.