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

The Convex combination Wikipedia article gives the following example:

Given a finite number of points $x_1,x_2,\dots ,x_n$ in a real vector space, a convex combination of these points is a point of the form

$$a_1{x}_1+a_2{x}_2+\dots +a_n{x}_n$$ is a convex combination if all real numbers $a_i\ge 0$ and $a_1+a_2+\dots +a_n=1$