I often go to the history of a concept for both historical appreciation and, practically, to understand it better. We often study Calculus without looking at what Archimedes was able to do -- break shapes into smaller parts -- and without really seeing how the notion of infinitesimals come into play. (Epsilon/delta definitions don't give the same insight.)
The natural log was discovered before e -- why would that be? Sine, cosine, trig functions -- they started as measurements of triangles, evolved into analytic definitions of their own -- why does this progression make sense?
In my mind, truly understanding a concept means you understood the path it took to the current state.