Nowadays we call them 'auxiliary verbs'. The name 'auxiliary' has a similar meaning to 'helper'. However, we now recognize these words as a grammatical class of verb with specific properties, not just because they precede a main verb, because they have some modal meaning, or because we can't use them on their own. The properties just mentioned may apply to other verbs which aren't in this group, and which don't have the same predictable grammar. Also one particular verb is now recognised to be in this auxiliary category - but doesn't have to occur with any other verb. This is the verb BE.
The important central properties which characterise auxiliary verbs are sometimes referred to as NICE properties. NICE is an acronym for:
Auxiliary verbs are necessary in English to make negatives with not. They also have a tendency to contract with the word not. If there is no auxiliary in the positive version of the sentence we use the dummy auxiliary DO:
- The giraffes can't stand up.
- We don't know what to do.
- They mustn't leave.
- The elephants aren't happy.
In the sentences above we see the negative particle occurring attached to the auxiliaries. When not contracted it must occur directly after the auxiliary in canonical negative sentences. Notice how the verb BE is fulfilling this function even though there is no following verb.
There are several instances in English when we need to invert the subject and auxiliary verb. The most obvious is in yes/no questions. Obviously we can only do this if there is an auxiliary! When there is no normal auxiliary in the declarative counterpart sentence we use the auxiliary DO:
- Can the giraffes stand up?
- Do we know what to do?
- Must they leave?
- Are the elephants happy?
Sometimes we delete material following an auxiliary verb leaving the auxiliary to stand in for the missing material. In answer to the questions above we can give the following answers. The missing material is in brackets:
- They can! [stand up]
- We do. [know what to do]
- They must! [leave]
- They are. [happy]
When wanting to add positive emphasis to a sentence, underlining that the sentence is true, we add emphasis by stressing the auxiliary, thereby giving it a full vowel (and preventing any contractions with subject pronouns). If there is no auxiliary in the canonical sentence we need to use the auxiliary DO:
- The giraffes can stand up.
- We do know what to do.
- They must leave.
- They are happy.
This grammatical class of words has two sub-categories. One includes the auxiliaries BE and HAVE which we use to form different aspects and voices - and the dummy auxiliary DO, which stands in in the present simple and past simple constructions, which don't have an auxiliary in canonical declarative sentences. The second group are the modal auxiliaries, of which there are nine central members and a few marginal verbs whose membership is debatable. The central members are can, could, may, might, shall, should, will, would and must.
This group of modal auxiliaries are probably the ones remembered by the Original Poster. These verbs plus DO, when followed by another verb, are always followed by an infinitive without to. They have other grammatical properties such as not being able to occur in standard English constructions with other modal verbs (i.e. you never have more than one per clause), not having inflected forms such as past participles, -ing forms, third person singular inflections and so forth. Depending on which grammar you subscribe to, you may feel that could is the past form of can and so forth, in which case you would regard them as inflecting for tense.
These verbs are most useful when regarded as a grammatical class of verbs distinct for their syntactic properties. It's not overly useful to lump in other words that we use to talk about necessity and obligation with them (I'm thinking of constructions such as have to used to talk about necessity and so forth, or going to in the going to future). The reason for this is that if we keep our classification of these verbs strictly syntactic and not semantic, we can very accurately predict their behaviour and offer clear and simple observations to students. These are a grammatical family of words, not a semantic one.
I agree with Papa Poule that the terminology used to describe these words is not important. However, the reason why they are the same type of words is very important for an understanding of English grammar.( If we want to be able to talk to other people studying the language though, then current terminology will, of course, be useful.)
Hope this helps!