An underlying space $|K|$ is the subset of $R^n$ which is the union of the simplices of $K$. While a simplicial complex $K$ is a collection of simplices s.t. every face of its simplex is in $K$ and the intersection of any two simplexes is a face of each of them.
My question is, why do I need the underlying space if I have a simplicial complex $K$. What's the difference between them? Could anyone give an explanation and examples (with a picture if possible). Thank you!