Femina vaccam amat.

Vacca feminam amat. 

What do these sentences mean and why has the ending changed on some of the words?

Does word order matter in Latin?

Femina vaccam amat.

The / A woman loves the / a cow.  

Vacca feminam amat.

The / A cow loves the / a woman. 

The ending changes to -am when the word is the object (having the verb done to it).

No, word order doesn’t matter in Latin. We look at the endings of the nouns to understand.