です is the polite form of is/am/are/be. It can also come after adjectives to make a sentence polite. ます is an ending attached to verbs, and functions to make the sentence polite.
> これは猫です。  
> This is a cat.  
> 昨日は暑いです。  
> Today is hot.  
> ケーキを食べます。  
> I eat cake.

Note that in the second example although the translation contains the word **is** this is contained in the adjective 暑い = "be hot". です does not mean **is** when it comes after an adjective, it just makes the sentence polite.

In the third example the verb 食べる (dictionary/plain form) becomes 食べます to make it polite.