What is the use of would in below sentences? [closed]

I would suggest this.

It would be great if you complete this.

Would is a Modal Auxiliary Verb, as are will, may, might, can, could, shall, should, and must.
As their name suggests, would and all other modal auxiliary verbs are used as auxiliary verbs.

An auxiliary verb is a verb that's used to introduce another predicate, usually another verb form. Modal auxiliary verbs must be the first auxiliary verb of any verb phrase they occur in, and must introduce (and be followed by) a verb in its infinitive form (but without to). See here for details.

In the sentences given above, would is followed by the infinitives suggest and be;
be itself is also an auxiliary verb, required by the predicate adjective great.