It simply means that it runs shortest path algorithm after pruning those links that violate a given set of constraints.
A constraint could be minimum bandwidth required per link (also known as bandwidth guaranteed constraint), end-to-end delay, maximum number of links traversed, include/exclude nodes.
CSPF is widely used in MPLS Traffic Engineering[citation needed].
The path computed using CSPF could be exactly same as that of computed from OSPF and IS-IS, or it could be completely different depending on the set of constraints to be met.
Consider the network to the right, where a route has to be computed from router-A to the router-C satisfying bandwidth constrained of x- units, and link cost for each link is based on hop-count (i.e., 1).