There are many reasons. Examination of the fingernails, for example, may reveal lung problems. COPD patients im advanced stages often have fingernails that curve downward. He also wants to examine the nailbeds to determine if you have good circulation. This isn't done much nowadays, but examination of the nailbeds used to be square one. He is also looking for tremor, of course, or palsy. He is also making a determination regarding your grooming. In Chinese medicine there is diagnosis on the basis of the lines in the hand. According to this theory certain patterns of lines are associated with certain genetic disorders, specifically cardiogenic problems. I have no opinion on this, but it makes some sense. The earlobes, for example, have shapes that are often associated with certain inherited disorders.
He/she probably wanted to see if you had any shaking.