Mutually exclusive environment is an environment in which the first segment of the two occurs only in such and such position, but the second segment never occurs in this same position. For further explanation we can see the following example in English language:
Voiceless [ r ] and [ l ] … (with open circles under are separated phonemes as indicated by minimal pairs in “ cloud” and “crowd”.
If we look at all the /l/ sounds we will see that they each have a different phonetically constrained environment, i.e they are in complementary distribution.
Velarized [ l ] occurs at the end of syllables
Voiceless [ l ] occurs after syllable initial voiceless consonants
[ l ] occurs elsewhere.
To make it easier to understand, we can use the “Clark Kent-Superman” analogy. Clark Kent and Superman are the same person, but they never appear at the same time. If Superman is present, then Clark Kent “disappears”, and vice versa. Therefore in our analogy, Superman and Clark Kent are allophones (the different realizations of phonemes in context, or variant sounds of the phonemic classes) that belong to the same person, in this case, the same phoneme.