Nominative case (mianownik)

The nominative case is the dictionary form.  If you look a word up in the dictionary it will be written in the nominative case.

The subject of a sentence will be in the nominative case.  The subject of the sentence is the thing doing the action of the verb.  

For the sentence: The man is talking Polish.  

Mężczyzna mówi po polsku*.  

the man, mężczyzna, is the subject.  He is doing the talking.  So, mężczyzna takes the nominative case.

You also use the nominative case after to when saying, "this is...".  to Piotr (this is Piotr)

and after jak (like) when making comparisons.  

*NB unlike English when we talk of the Polish language in Polish itself, the p of polsku is not capitalised when used as an adjective.