The convex hull of a set $X$ in an affine space over the reals is the smallest convex set that contains $X$. When the points are two dimensional, the convex hull can be thought of as the rubber band around the points of $X$.

As per Wikipedia, a convex set is the smallest affine space closed under convex combination.

A convex combination is a linear combination where all the coefficients are greater than 0 and all sum to 1.