From Rotman's Algebraic Topology:
An oriented simplicial complex $K$ is a simplicial complex and a partial order on $\text{Vert}(K)$ whose restriction to the vertices of any simplex in $K$ is a linear order.
I don't understand how I would come up with an example for this.
If you took $K=\{\Delta^3, \Delta^2, \Delta^1, \Delta^0, \text{all faces of simplexes}: \Delta^i \cap \Delta^j = \emptyset, \text{ for $i,j \in \{0,1,2,3\}$} \}$.
How could you define a partial ordering on $\text{Vert(K)}$? And how would you define a linear order for any restriction to a simplex?