Applicatives model computations in which values computed by subcomputations cannot affect what subsequent computations will take place. Relative to monads, this restriction takes power away from the user of the interface and gives it to the implementation. In particular, because the structure of the entire computation is known, one can augment its definition with some description of that structure.
For more information, see:
Applicative Programming with Effects. Conor McBride and Ross Paterson. Journal of Functional Programming 18:1 (2008), pages 1-13. http://staff.city.ac.uk/~ross/papers/Applicative.pdf