Sometimes, especially on this forum, I am wondering wether I should say "what does it mean" or "what does it means" ? And should I say "it means that..." or "it mean that..." ?
Here are the relevant rules:
A clause never has more than one finite verb - a verb that is marked for tense, person and number (to the extent that it can be marked for any of these categories.
When the verb (predicator) in a finite clause is constructed with auxiliaries (helping verbs), the finite verb is always the first auxiliary in the chain.
Each auxiliary verb licenses specific non-finite forms (present or past participle or infinitive) for the following non-finite. For instance BE licenses either a present or past participle, HAVE licenses a past participle, and so forth. Auxiliary DO licenses only an infinitive.
In questions, the subject and the first, finite auxiliary switch places; if there is no auxiliary, the ‘dummy’ auxiliary DO is introduced (this is called *DO-support'), and takes the appropriate finite form.
In your question, DO-support is invoked to provide an invertible finite auxiliary, does. It must be followed (after the subject) by the infinitive form of the lexical verb MEAN:
What does it mean?
In your answer, DO-support is not required; MEAN is the only verb and takes the finite form which bears the desired tense (present) and agrees with the subject in person (3d) and number (singular)—means.
It means that ...