An auxiliary verb is one which helps other verbs to make tenses, passive forms etc. There are two groups - primary auxiliaries and modal auxiliaries.
Be, do, have and their various forms are called primary auxiliaries.
Be is used with other verbs to make progressive and passive verbs forms.
- I am writing.
- He was punished for lying.
Do is used to make questions, negatives and emphatic forms of non-auxiliary verbs.
- Do you know where John lives?
- I dont know.
- Do sit down.
Have is used to make perfect verbs forms.
- I have completed my work.
- She has acted in a film.
- They had forgotten to send the letter.
Primary auxiliaries merely help to express statements of fact.
- She is writing.
- I am working.
- You have done wrong.
- He did not come in time.
- They have arrived.
Note that be, do and have can also function as principal verbs. They are called auxiliaries only when they help other verbs to form their tenses and moods.
- You were wrong. (Principal verb)
- You have done wrong. (Auxiliary verb)
- She is a good singer. (Principal verb)
- She is singing. (Auxiliary verb)