One of the main reasons that this virus (as well as many others) is especially dangerous to older individuals is that our immune system becomes less effective as we age. This process is called immunosenescence, and it basically means that older people are more susceptible to anything that the immune system would normally defend against - including infections, as well as cancer. Unfortunately, this still applies even to older people who are otherwise in good health.
So, while a healthy senior is probably not in as much danger as another elderly person who is also, for example, diabetic, or has a heart problem, you are still in more danger than you would have been at age 35 or 45.
We can see this by looking at the rate of death by age group in COVID-19 patients in the US. According to the Centers for Disease Control and Prevention, as of March 16, a total of 4226 cases of COVID-19 had been documented in the United States. Of these cases, fatality was highest in persons aged ≥85, ranging from 10% to 27%, followed by 3% to 11% among persons aged 65–84 years, 1% to 3% among persons aged 55-64 years, <1% among persons aged 20–54 years, and no fatalities among persons aged ≤19 years.
Drafted 3 April 2020