One example would be a map induced by a morphism `f: X \to Y` in the long homology sequence. 

E.g. suppose the top row is a cohomology of pair (X, A) and the bottom row is the cohomology of pair (Y, B). Then the theorem says that the `H^n(X, A)` can be squeezed between the n-th and n-1-th cohomology of X and A, because any morphism inducing isomorphism on those extends to `H^n(X, A)`.