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"?


A short update to precise what I mean (literally that's the comments below): 

The meaning of "combinatorial" for *abstract simplicial complexes* is pretty easy to see: indeed, a data consisting of set of vertices $V=\{ v_1,v_2,...,v_n \}$ and a $m$-simplex of $S$ is defined as a subset $\{ v_{i_1},...,v_{i_m} \}$ of $V$. then a subset $S$ of power set $P(V)$ of $V$  is called abstract simplicial complex if for every $m$-simplex $\{ v_{i_1},...,v_{i_m}\}$ contained in $S$ every subset $\{ v_{i_{j_1}},...,v_{i_{j_d}} \}$ is (as a $d$-simplex) is contained in $S$.

Therefore obviously not every subset of the power set $P(V)$
of $V$ is a abstract simplicial complex. So to determine which subsets of $P(V)$ can occure as abstract simplicial complexes is a combinatorial problem. 

But how to draw the same analogy to cech cycles isn't clear to me. Is it possible to associate abstractly a abstract simplicial complex to a Cech cycle in order to "make" it combinatorial?