@Preben Alsholm Preben, these formal definitions should provide everything that you need to know for this question. I only post this because you said that you know next to nothing about graph theory. So, sorry if this is already familiar material.
Definition 1: A partition P of a set S is a set of nonempty pairwise-disjoint sets whose union is S. The members of P are called the blocks of the partition.
Definition 2: A coloring of a graph is a partition of its vertices such that no two vertices in the same block share an edge. If the coloring has k blocks, it's a k-coloring.
Definition 3: The chromatic number of a graph G is the minimal k such that G has a k-coloring.
Definition 4: A k-clique of a graph is a k-subset of its vertices such that every pair of those vertices share an edge.
Definition 5: The clique number of a graph G is the maximal k such that G has a k-clique.
Obvious Theorem: For any graph G, CliqueNumber(G) <= ChromaticNumber(G).