What do they do?
They help the other verb to make sense, as Colleen said. An auxilliary verb is the junior partner in a sentence with several verbs. Mostly a form of to be or to have.
In "I have found my key" to find is the main verb and to have is the auxilliary, the "junior partner". In "I have a key" "to have" is the main verb.
Basically, without them, the main verb is difficult to understand ... for example, "She *is* walking home" ... without the helping verb, you have "She walking home" , which is not a proper sentence.
Moreso, without the auxiliary verb, you would have to say "She walks home" which has a different meaning altogether.
Helping verbs are also called "auxiliary verbs".