Learn Polish: Nasi klienci to kobiety i mężczyźni.

Nasi is the "virile" (masculine personal) plural form of "our". You must use it whenever the plural group includes at least one man. If the clients were known to be entirely female, you would use the non-virile form nasze instead.

How does the word klient change into the plural klienci?

Masculine personal (virile) nouns often change their final consonant in the plural. Here, the hard -t at the end of klient softens into -ci. This is a very common sound change for this group of nouns.

Why do we use to here instead of są for "are"?

When you are simply saying that "Noun A is Noun B" (defining one thing as another), Polish commonly uses to as the linking word. The big advantage of using to is that the nouns on both sides stay in the basic Nominative case, meaning you don't have to change their endings!

Mężczyzna (man) ends in an "-a" in the singular. Does that affect its plural form mężczyźni?

Yes! Even though mężczyzna looks like a feminine word because of the -a, it refers to a man, so it behaves as a virile noun. In the plural, the ending -zna softens to -źni to create mężczyźni.