Biological, or physiological, age is a measure of how well or poorly your body is functioning relative to your actual calendar age.
For example, you may have a calendar or chronological age of 65, but because of a healthy and active lifestyle (avoiding longevity threats like tobacco and obesity), your body is physiologically more similar to someone with a chronological age of 55. Your biological age would therefore be 55.
While not an exact science, the concept of biological age can incorporate objective measures like resting heart rate, blood pressure, and visual acuity, as well as more subjective criteria like ease of performing daily tasks, muscle strength and general mobility.
Wahlin A., MacDonald S.W., deFrias C.M., Nilsson L.G., Dixon R.A.. "How do health and biological age influence chronological age and sex differences in cognitive aging: moderating, mediating, or both?" Psychol Aging. 2006 Jun;21(2):318-32.