This is called a plural possessive. It means belonging to more than one family. Here are some sentences.
The families lived on sharecropping land
Ten families were effected by the storm. The storm affected ten families.
The coming of winter gave a new impetus to the appeals for food and clothing for needy families.
Genealogy is the the study of the history of families and the line of descent from their ancestors.
turmoil In the turmoil of the earthquake many people lost their families.
I have lots of families
During the great depression, many families had to survive on gruel stale bread!!
Several families vacationed together.
You would use "family's" if you are saying they own something, such as:"That family's house is big!!"Or, if you used "families" you would be using it because you are saying that there is more than one family, such as:"There are a lot families in the picnic area."Hope this helped!
cultivate in our families
The deprivation of families during the Great Depression lead them to living in run down slum areas.
Workers said they were instructed not to talk with families of the elderly they were caring for and not to fraternizewith one another.