A subset X of Rⁿ (or any vector space over a field of characteristic 0) is called star convex iff it contains some point a∈X such that for any x∈X the entire segment [a,x] = {tx+(1-t)a : 0<=t<=1} is contained in X.

That is, there's a point from which you can "see" all of the set.

Star convex sets needn't be convex (think of a 5-pointed star!), but any convex set is star convex (indeed, you can take a to be any point in the set).