The word même is extremely common and versatile in French, with many meanings depending on its position and/or context. The best way to understand it is to see it in action.
Même as an adjective = same / itself / very - exact / precise
Note that when même is used as an adjective, it agrees in number : même(s). Its meaning can vary from same / itself / very to exact / precise.
Même as an adverb = even
Note that when même is used as an adverb, it never changes : même. Its meaning in this context is even.