thesaurus.maths.org

If a figure has a hollow, going in like a cave, it is concave.
You can test for concavity by picking two points inside the figure and joining them together with a line; if for some pairs of points the line goes outside the figure, it is concave.
A polygon is concave if it has an interior angle which is greater than 180 degrees.

Curved inwards.
A function f is called concave if f(tx+(1−t)y) ≥ tf(x)+(1−t)f(y) whenever x and y are in the domain of f, and t is in [0,1].
In other words if a straight line is drawn so as to cut off a piece of the curve, the piece cut off will lie entirely above the line.

A real function f is concave if −f is convex.