I have no idea in detail but: Handsomeness oftentimes is traits which say you are healthy. Eg not being starving-thin nor unhealthy obese, having nice hair and skin (enough nutrients eaten), having a youthful look (the younger you are the less likely you get ill and the better you are fit for reproducing (more so as a woman)), having a good body posture and normal body features (again, nutrients and maybe even genetical disadvantages of anatomic stuff), red cheeks meaning you are young and not ill, nice eyes again if eyes are yellowish you may be ill/malnourished... So almost everything we call handsome is a sign of healthiness and fitness. There are much more factors.

I dont know if handsome people are healthier, I doubt it as many illnesses are coincidences/mutations or due to life circumstances. But I guess you can say people who are seen as beautiful almost never have visible health-flaws such as genetic disorders or other (genetic and visible) disabilties. Evolution made us find healthy people beautiful. And young people also. Simply because thats the best way to be sure to reproduce and have your genetic material live on.