Crypto Algorithm Evaluation - Katz, Sahai and Waters Predicate encryption scheme

Reading through this paper by Katz, Sahai and Waters "Predicate encryption supporting disjunctions, polynomial equations and inner products" (i have been notified that i cannot post the link )
wondering if anyone can explain the encryption scheme? ie what each of the elements of the cipher text/secret key do, i understand that some elements are used to mask others, but a detailed explanation of the essence of this scheme would be appreciated