I think to answer your question it needs to be broken into two parts, namely "what is です's etymology?" and "where is です used?".
You will see です used in two ways:
As the polite form of the copula だ. In this case, it has the meaning "to be" and acts mostly like a verb, in that it inflects.
"He is a doctor."
"It was a little weird."
As a polite marker for i-adjectives. Historically, i-adjectives had a polite inflection, 〜うございます, which showed up as late as the 1960s, but it was thought to be "too polite" in many cases and was eventually discarded. However, the non-polite form was considered to be too impolite, so 〜です was added on the end as a polite marker. It is not the copula here and as a result does not inflect.
"It is fun."
"It was hot."
Although there are many theories about the origin of です, the common one among linguists I know is that it is a contraction of でございます. However there are competing theories (でそう、であります) and there is not yet a consensus about the correct one.