Being a part of social functions, such as a walking group, helps the elderly by preventing isolation and loneliness while promoting positive self-awareness. Being a part of a walking group would also help to develop a support system for the individual, which has been linked to positive psychological and physical effects. Such support systems help to alleviate stress and prevent depression or anxiety. Being a part of a physical group activity also prevents muscles from deteriorating. This enables the individual to stay independent, which has a cyclical effect by encouraging the individual to become involved in more group activities in the future. All of the above increase one's quality and satisfaction of life.
The two links below echo what was stated above. I would also encourage you to read Motivating Elderly People to Exercise Using a Social Collaborative Exergame with Adaptive Difficulty by Dale Cantwell, Daire O'Broin, Ross Palmer, and Greg Doyle.