Proprioception is the ability of the body to sense it’s place in space. Proprioceptors are mainly located in joints, they are receptors that detect and tell the central nervous system the position of an arm or leg in space. For example, if someone asks you to close your eyes, and they raise your right arm over your head, proprioceptive receptors in your arm are telling your brain that your right arm is above your head. I think we should ask more questions as to the role proprioception plays, along with it's relationship to our brain (central nervous system) and bodies (motor function).
Great, but what does this have to do with falling?
Without proprioception, our bodies would not be able to react appropriately to the environment around us. For example, when we walk in the dark or on uneven surfaces such as sand, our bodies have a heightened sense of awareness that help prevent us from falling down. This heightened sense of awareness is a series of complex functions between the body and the brain that allows us to respond with the (hopefully) correct reflex to our environment.
What is the significance of proprioception to the problem of falling and the elderly population?
Research indicates that a decline in proprioception in the elderly population is correlated to incidents of falling and “reduced functional independence.” 
Research has also shown that proprioceptors decline as we age. “Joint position sense becomes more accurate through childhood and adolescence, peaks in young adulthood and then progressively deteriorates after this.”  This decline is caused by many factors, primarily because the functions of the nervous system begins to decline (see Neuroplasitcity). In addition, proprioceptive function is negatively impacted in the elderly when their brains are required to focus on more than one task:
“Older adults performing complex movements have been shown to have an excess of central activity compared with younger adults and that this is predominantly in regions associated with movement-related proprioceptive feedback. When attention is diverted from the proprioceptive task in hand this appears to have a more significant effect on older people. So older people show greater cortical activation than younger people for the same tasks and their proprioceptive acuity is more affected when attention is divided. Whether this observation reflects a compensatory mechanism for loss of peripheral proprioceptors, or for decreased putaminal activity or indeed another factor entirely remains to be seen.” 
Interesting conclusions drawn from the article cited :
The authors of the article note that the following areas may help with stimulating increased proprioception in the elderly:
- Development of a proprioceptive biomarker (a tool to assess and measure)
- Develop proprioceptive specific exercises
- Therapeutic joint taping (to encourage stimulus of proprioceptors that are weak or asleep)
- Develop specialized footwear (to encourage stimulus of proprioceptors through activation of specific muscles/reflexes)
 Suetterlin, Karen Joan and Avan Aihie Sayer. “Proprioception: where are we now? A commentary on clinical assessment, changes across the life course, functional implications and future interventions.” Age and Aging (2014) 43 (3): 313-318, <https://academic.oup.com/ageing/article/43/3/313/16765/Proprioception-where-are-we-now-A-commentary-on>