It means the cow is female. "La" is the single female version of "the". In Italian and other languages nouns have a natural gender, male or female and frequently neuter, although I haven't yet seen the latter in Italian. Cows are always female, so they have "la" if single and "le" if plural. Bulls are male so they have "il" and "i". Hats are male and belts are female, so the hat is "il cappello" and the belt is "la cintura."
It has to do with grammatical gender, which is foreign to English. Languages such as Italian and Greek and Spanish have possessives agree in gender and number with the noun they accompany, that is, with the thing possessed, not with the possessor. English lacks grammatical gender and puts possessive with the one possessing with pronouns his/her/its. To an English speaker, it just "makes sense" and is clear, but in fact for many languages on the planet, grammatical gender is clear. So in Italian, to say "her son," you must say suo figlio, because figlio is masculine. Il ragazzo è suo figlio, can refer to either his or her son, depends on context. Similarly, Sua figlia è cortese, "his daughter is polite," it must be sua to match the gender and number of figlia. Whether it is his daughter or her daughter entirely depends on context. DL has short sentences without context, which is really the heart of the problem in this learning platform. Spanish speakers also use su for his or hers depending on context. Whether su perro is her or his dog can only be determined by context. Me quedé en su casa, "I stayed at her/his house."