What is Rim Offset and Backspacing? How Do They Affect Fitment?

Many drivers are familiar with rim diameter, bolt pattern and center bore, but not offset and backspacing. Offset is the distance between the mounting pad and rim's midpoint. The diagram attached shows a wheel with a positive offset. Every contemporary Original Equipment wheel has a positive offset, however O.E. offset varies. 

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What happens when you get a new wheel with a different offset?  A higher offset results in the wheel and tire moving more in (towards the hub). A lower offset causes the wheel and tire to move out (towards the fender).