A worst-case analysis looks at an algorithm and determines the slowest running time possible given a worst-case input (e.g. sorting problem - the array is sorted backwards, or some algorithm-specific worst-case). The worst-case runtime guarantees that the algorithm won’t run any slower than this.
Note that worse-case runtime is no grounds for completely rejecting an algorithm, e.g., it might still be worth considering an algorithm that has an atrocious worst-case runtime that can only be caused by a very unlikely worst-case input.