Dentistry is generally divided into many subdivisions. Some of these areas are legally defined specialties that usually require the dentist to have completed a 2 year (or longer) postdoctorate in their chosen area. Other areas are not legally defined, but rather they are categories of dentistry that a dentist may choose to focus on.
Dental practices that advertise themselves as a Family Practice are most most often a combination of the two. The dentist is likely to have specialized in General Dentistry (a specialization of its own), and is interested in providing routine dental services for entire families.
This enables them to provide a much broader range of services, while also enabling them to focus on particular areas of interest should they wish. For example, a General Dentist may define themselves as a Family Practitioner, but also offer services to families in a certain area of dentistry such as Implantology (dental implants).