We use auxiliary verbs (do, have, etc.) or modal verbs (can, must, etc.):
1. To avoid repeating the main verb / verb phrase.
2. With so & neither to say that someone or something is the same.
Use so + auxiliary + subject with a positive verb, and neither (or nor) + auxiliary + subject with a negative verb.
3. To say that someone or something is different.
4. To make 'reply questions', to show interest or surprise.
5. To show emphasis in a positive sentence.
It is often used when you want to contradict what somebody says. With the present / past simple, we add do / does / did before the main verb. With other auxiliaries, e.g. be, have, will the auxiliary verb is stressed and not contracted.
6. To make question tags.
It is usually used to check information.
We use a positive auxiliary with a negative verb and a negative auxiliary with a positive verb.
Question tags are often used simply to ask another person to agree with you, e.g. It's a nice
day, isn't it? In this case the question tag is said with falling intonation, i.e. the voice goes down.
Question tags can also be used to check something you think is true, e.g. She's a painter, isn't she? In this case the question tag is said with rising intonation, as in a normal yes / no question.
Source: English File, Upper-Intermediate
by Chritina Latham-Koenig and Clive Oxenden