です

In its most basic form, です means "to be".

学生です : student is = (I) am (a) student, but also: (they) are (a) student(s).

The subject is understood from the context; Japanese speakers feel no need to state what is obvious.

Though, if it is needed to specify what です refers to, you can use the particle は in the structure A は B です = A is B.

私は学生です : I am a student

The real literal meaning is then closer to "as for A, it is B". は does not put an emphasis on the subject. You mention it purely to make what you're talking about much clearer.

But it's sometimes only a politeness marker

It's the case if there's already another verb (or something that acts like a verb, like an i-adjective) in the sentence. For example:

• 赤いです : it is red
• 赤かったです : it was red

Here, if you have to change the tense of the sentence, you'd change the tense of the i-adjective because that adjective already means "is/was red". There's no need to add another verb: です is purely there as a politeness marker.

This grammar point is touched on in Duolingo lesson 1 and Genki 1 - lesson 1.