It’s a bad word for a piece of code, and you should feel bad for using it. Here is why:

1. It is easily phonetically confused with “rapper”

Well, this one is actually funny. Really the only redeeming quality. So if someone tells me that they “made a wrapper”, I immediately giggle a bit inside.

2. Wrapping things is a programmers job.

As programmers, we are in the business of abstractions, and a function clearly is an abstraction. A function that calls something else wraps that something else. So isn’t everything a wrapper?
Who would say that the following function is a wrapper?

template <class T>
T multiplication_wrapper(T a, T b)
{
  return a * b;
}

It does wrap the multiplication operator, does it not? Of course, the example is contrived, but many people call equally simple functions “wrapper functions”.

3. It is often a bad analogy

When you wrap something, like a present, you first need to unwrap it to actually use it. So in that case, it acts more like a kind of envelope. This is clearly not the case for what most people call wrappers. You could wrap some data in a .zip file – that would make sense! But no one uses it like that.
Another use of the word wrap implies something that goes around something else, forming a fixture of sorts. Like a wraparound baby sling. So I guess this could work for some uses, like a protection layer. Again, it is not used like that.
Finally, there’s wrapping up something, as in finishing something. Well, maybe if you’re wrapping your main function around the rest of your code, you can finish writing your program. A very monolithic approach.

There are plenty of better alternatives

In most cases, what people should rather use is either facade or adapter. Both names convey a lot more meaning than wrapper. A facade is something that wraps code to make the interface nicer. An adapter wraps an interface to integrate with some other piece of code. Both are structural design patterns. Both wrap something. But then again, that could be said for all of the structural design patterns. Or, most code. Except maybe assembler?

So please, calling something a wrapper is not enough. You might as well just call it function/object/abstraction. Use adapter, facade, decorator, proxy etc.. The why is more important than the what.