What are lexical sets?
A lexical set consists of a group of words all of which have the same pronunciation for a certain sound in a given variety. For instance, the lexical set TRAP is used to refer to the pronunciation which speakers of a variety have for the sound which is /æ/ in Received Pronunciation. So if speaker uses [a] or [ɛ] in TRAP it is taken that they will use [a] or [ɛ] in all other words which contain this vowel, e.g. BAD, LATTER, SHALL, that is, in the words which comprise the lexical set. The advantage of this is that instead of saying the realisation of the /æ/ vowel in variety X, which phonetically can be quite far removed from [æ], one can refer to the vowel in the lexical set TRAP.
The original group of lexical sets was presented in John Wells' three volume work Accents of English (Cambridge University Press, 1982). These were intended to cover the vowels of Received Pronunciation and their realisations in accents of English throughout the world. However, the group is not always appropriate for the description of varieties far removed from Received Pronunciation. For this reason many modifications and additions to the original lexical sets have been proposed, especially as Wells' lexical sets only refer to vowel values.