Why was there a need for Martin-Löf to create intuitionistic type theory?
Very briefly: the simply-typed $\lambda$-calculus does not have  dependent types. Dependent types were proposed by de Bruijn and Howard who wanted to extend the Curry-Howard correspondence from propositional to first-order logic. The key contribution of Martin-L&ouml;f's is a novel analysis of equality.
There are two main ways of giving Curry-Howard style account of equality. 


Using Leibniz's rule of the identity of indiscernibles to encode propositional equality . This approach is used in the calculus of constructions, but it requires impredicative universes which were rejected by Martin-L&ouml;f for philosophical reasons.
A direct constructive characterisation of equality. Giving such a characterisation using identity types might be the main novelty of Martin-Löf's intuitionistic type theory.


Identity types appear deceptively simple today, but they refocussed the understanding of type-theory partly because they gave rise to intriguing semantical questions such as: are identity proofs unique? In some sense this question lead to homotopy type theory and the univalence axiom (which is incompatible with the uniqueness of identities). That the uniqueness of identity proofs is not derivable in Martin-Löf's intuitionistic type theory was shown 
by Hofmann and Streicher in: "The groupoid interpretation of type theory". Incidentally, this result also shows that pattern matching is not a conservative extension of traditional type theory.