Consider a telescope finderscope as a much smaller telescope that is attached to the main telescope to help you line up the telescope with an object of interest.
To answer the question…

What is a finder scope on a telescope?

A finderscope on a telescope is a small scope with a magnification generally smaller than that of the main telescope, but with a much field of view so that it helps with slewing a telescope towards a desired astronomical object. 
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