What part of speech is the verb did?

'Did' is the past tense form of both the main verb 'do' and of the auxiliary verb 'do'.

e.g.,

1. "He did his homework" (main verb)

2. "Did he do his homework?" (auxiliary verb)

3. "Yes, he did do his homework!" (auxiliary verb)

Auxiliary verbs are sometimes called 'helping verbs' because they appear alongside the main verb in a sentence. They are moved in front of the subject of a sentence to produce yes-no questions (as in examples 2 and 3 above).