"My grandfather is healthy today."
Translation:मेरे दादा आज स्वस्थ हैं ।
As a show of respect, words referring to people older than you or in a position of authority are treated as if they were plural. So, even though मेरा दादा is grammatically correct, it would be seen as rude.
This is also the reason this sentence uses the plural form हैं instead of the singular है.