In Lectures on Discrete Geometry, Matousek writes (p.11) (excerpt here):
It is very tempting and quite usual to formulate Helly's theorem as follows: "If every $d+1$ among $n$ convex sets in $\mathbb{R}^d$ intersect, then all the sets intersect." But, strictly speaking, this is false, for a trivial reason: For $d \geq 2$ , the assumption as stated here is met by $n = 2$ disjoint convex sets.
I don't understand what is wrong, and the given counterexample?
Counterexample: $n=d=2$ and you have a collection of $n=2$ disjoint convex subsets of the plane. Then the condition "every $d+1$ intersect" is trivially (vacuously) satisfied. Yet clearly not all the sets in our collection intersect.
In the correct statement of the theorem we assume $n>d$, so that the condition about $d+1$ sets intersecting is nontrivial, i.e., it actually means something.