What is the defining Set in NLP
If you read the following sentence at the first line of section 6:


  The debiasing algorithms are defined in terms of sets of words rather than just pairs, for generality, so that we can consider other biases such as racial or religious biases.


$D_1, D_2, \ldots, D_m$ are the set of words, in general, to be considered in the de-biasing algorithm, instead of considering a pair of words such as Computer Programmer and Houseworker for the de-biasing genders of man and woman. Hence, one of $D$s could be {'Computer Programmer', 'Houseworker'}, here, as an example.