In its everyday usage, inverse means opposite. The mathematical meaning of inverse is closely related to this everyday meaning.
There are two common usages of the word "inverse" in mathematics: the first is in the "inverse of a number", which means "one over" the number. So for example the inverse of 2 is 1/2, the inverse of 2/3 is 3/2, and so on. This can be thought of as "inverting" the fraction, i.e. turning it upside-down.
The second usage of the word "inverse" is in relation to functions. We know that a function represents an action that can be carried out on a number.
Well, for every function or action there is a corresponding " inverse function", which undoes that action. Of course the result of the inverse action is the original number you first started with!
For example, the inverse function to the function "multiplication" is "division", because that's the action which takes you back to the original value. You can see that the inverse function can be thought of as a sort of "opposite" function, as in the everyday usage of "inverse".