what is the meaning of derived and non-derived environments in phonology? for example, non derived environment blocking, that does it mean? I've looked everywhere but I could not find the actual meaning I could only find related theories and effects.
A derived environment is a phonological context that exists because of a rule or process. For example, the English plural noun "socks" in the sentence "I have white socks" has a final [ks] cluster that results from the plural-forming rule or process which adds [s] to the end of the word, so the [ks] cluster in socks is in a derived environment.
In contrast, the singular English noun "ox" also ends in [ks], but here there is no process or rule that created the consonant cluster. It just existed from the start. So here, the [ks] cluster occurs in a non-derived environment.
The answer by Brass Tacks is basically correct, but could still be elaborated on for the sake of clarity. The concept was introduced in Kiparsky 1972 in a paper "Abstractness, opacity and global rules" (published by IULC), in an attempt to explain why in Estonian /lugu/ → [loo] "story" but /luu/ "bone" does not undergo vowel lowering. The explanation offered is that the conditions for applying the lowering rule are satisfied in the underlying form (but the rule does not apply), whereas in other cases where the rule does apply, that is because conditions for applying the rule are not present in the underlying form. This notion of "derived environment" and the motivation for empowering grammar with such look-back abilities is discussed in section 1 of that paper.
The concept is relevant because there is a claim that certain rules only apply in a "derived environment". Two things play a role in determining whether a given string is a "derived environment". One is that at least two elements of the structural description are members of different morphological constituents, e.g. plural -s in sock+s. The other is that some property required by the rule only comes about by previously applying some rule, for example in Finnish, t→s/__i which applies to [vesi] ← veti ← /vete/, where final /e/ becomes [i] (thus creating the [i] that triggers the assibilation rule). Assibilation does not apply to /æiti/, because that root is monomorphemic and the potential trigger /i/ does not result from applying a rule.
The evaluation of "in separate morphemes" or "is derived by applying a rule" is carried out with respect to the cycle, therefore the grammar only looks back to morpheme divisions present on the current cycle, or phonological properties in the input of the current cycle – not the properties present in the lexicon.