I saw several times that often some data describing certain algebraic objects, eg the set of cells of a simplical complex or a Cech cycle of a chosen coving of a variety are called "combinatorial data" or "encoding combinatorial data".

My question is simply what is the justification of the name "combinatorial" here? what is combinatorial on these data?

More generally can it be precised when a certain data describing an algebraical object is called "combinatorial"?