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)
.