It can be thought of as "What if...?"
What if the headwinds are stronger than expected?
What if an engine fails after V1?
What if the destination airport is closed for some reason?
Each of those is a "contingency" - a possibility that will require a "Plan B" - a change in operation from the original plan, to accomodate the changed situation.
"Concorde could fly non-stop Caracas - Paris, contingent upon the winds and weight." Meaning that normally it could not, but if the winds and weight - the contingencies - were abnormally favorable, it could.