(Quote) There is a difference in clearance and tolerances, Tolerances are the minimum to maximum clearances needed to operate. Clearances are the actual dimension between the two parts when placed together. J E CUSTOM
JE, I don't think I could teach you much. I'm just using your reply as a teachable moment for others reading this. I feel a need to help with the terminology.
Actually, the word tolerance as used in part drawings isn't really limited to any of the things others have described here.
The engineering definition is basically "the permissible limit or limits of variation in a physical dimension; a measured value or physical property of a material, manufactured object, or system; or other measured values (such as temperature, humidity, etc.). As we use the term in gunsmithing, it usually means the permissible limits of a given dimension usually expressed as + or - a small amount (eg 0.7000 +0.0002/-0.0005).
Tolerances in our world are usually needed to make sure parts can be interchangeably assembled and still work properly. We need to be able to make sure that a bolt fits our assembled barreled action. In fact, in an ideal world, all bolts and actions of a given make would have interchangeable bolts because the tolerances would be specified such that all bolts would fit all actions and always result in acceptable headspace. In the real world this never happens except for the best custom actions (and even then is not good practice).
A good way of understanding the need for tolerances is to compare the Sammi standards for cartridges and chambers. The Sammi standard for cartridges specifies the maximum cartridge in such a way as to ensure that it will always fit inside the minimum Sammi chamber. It is important for hunters to know that they can buy a box of ammo off the shelf and know that it will fit in their rifle, and that's one of the main reason such standards exist.
In the world of precision smithing, we have fewer applications for tolerance because we are always striving for zero. For example, I always align barrels in my lathe aiming for zero axial concentricity or as close to zero as I can get. But I think many smith's are happy with a half thou or so, and I have seen many examples on line where some smith's don't even do a true axial alignment so lord knows what their tolerance really is.
As JE said, clearance is simply the space between two assembled parts. But beyond that, clearances can actually have tolerances (eg 0.0020 +0.0002/-0.0001), but tolerance can never have a clearance.
In bigger more complicated assemblies, tolerance stack up also becomes important since an assembly built of components all at their maximum tolerance can be significantly bigger than an assembly made with all minimum tolerance parts. Or worse yet, the end result can be that they stack up so badly that the final assembly can be assembled. Most assemblies will be built with parts all over the map. So the Tolerance stack up for all the parts is analysed and modified to ensure that the worst case can still be assembled and still works as intended. That's basically how tolerance came to be such an important quantity.
I suppose I could put together a complete paper on the subject, but it would take days to do it properly. The above ought to be plenty enough to help those here who are wondering what all the fuss about tolerance is all about!