This theory does not attempt to claim that all human languages have the same grammar, or that all humans are "programmed" with a structure that underlies all surface expressions of human language. Rather, universal grammar proposes that there exists an underlying set of rules that helps children to acquire their particular language(s).
Students of universal grammar study a variety of languages' grammars with the purpose of abstracting generalizations, often in the form of "If X holds true, then Y occurs." These have been extended to a range of traits, from the phonemes found in languages, to what word orders languages choose, to why children exhibit certain linguistic behaviors.
Three linguists who have had major impacts in this area, either directly or through the schools of thought they promulgate(d), are Noam Chomsky, Edward Sapir and Richard Montague.