Family units are created so that there will be someone to socialize the children.  Families are important because they can do stuff like teaching the children what is expected of them.  You can see them doing this early on in the book when Jonas's parents are reasoning with Lily about her being angry at the boy from the other community.

The families are formed by appointment.  The Elders tell you who your spouse will be.  They decide when you are ready to have kids.  They have made the rules saying you get two kids, one of each sex.

There's a quote on page 8 about people not being given spouses because they don't have the right personalities.