Why do humans have toenails?

Toetails are mostly considered to vestigial which means that they once had once function which has been reduced of eliminated. It helps to look at other primates closely related to humans like chimpanzees.
Chimp feet are more similar to our hands than our feet, and it is likely that our ancestors had a similar arrangement. 

 Chimps climb trees and swing from branch to branch, which is a complicated task requiring a great deal of coordination. The switch to obligate bipedalism (walking on two feet) probably is what caused our feet to change. 

When climbing the nail provides a counter force when gripping a surface, which enhances important sensory information for someone traveling by tree. Our fingertips are some of the most sensitive  parts of our bodies, and the same was probably true of our ancestors toes. 

On a hand-like foot the toenail also allows for finer manipulation of objects, like grooming another animal, or making tools. 

We also use our toes for balance while walking and nails probably aid in increasing the sensitivity of our proprioception.

I lost the nail on one of my big toes once. I was lucky that it grew back mostly. But during that experience I discovered excellent reasons for that nail, so I would not call it vestigial at all. I found the nail served a very useful, small but very useful, protective function for my toe. Having some protection at the ends of our appendages, which will generally be the first things tht come into contact with objects, is useful.
Most things that people label vestigial still serve some function, such as the appendix, which has been long falsely considered a vestigial organ. Most of the time it just means that we haven't figured out what it does.

I don't use vestigial to mean "useless," the meaning I'm going for is something more like "reduced." Which is to say I mean that they serve a different function than the one they may have served in our recent evolutionary history. 

Since all species are constantly changing and features may serve different functions at different times, maybe vestigial has connotations that I don't intend.

Ah, ok. Vestigial is often used to mean a loss of function, but I agree with the connotation you intended.

An exaptation is something that had one function (or multiple), but is then used for something else and its further evolution is driven by the new function. Although this isn't quite the same as "reduced". Certainly our toenails have become reduced over time, which would seem to indicate that the functions that we used them for are not as important as they once were. I suppose we might say that the function and resulting structure have atrophied (obviously not completely though) or have become attenuated.