What is the object of a gerund?

If by “object of a gerund” you mean “purpose of a gerund”, then a gerund is a way of converting a verb into a noun (by adding the …ing suffix).
If you meant “object” in the sense of a grammatical construct then the expression “object of a gerund” doesn’t have any meaning. “Objects” are (grammatically) and “gerunds” are nouns.
“Gerunds” can be (grammatical) “objects” (or “”) but they don’t have “objects”.
Examples of gerunds:
##color(white)(“XXX”)##Climbing the hill required a lot of effort.
##color(white)(“XXXXXX”)##(used as a subject)
##color(white)(“XXX”)##The boy enjoys playing.
##color(white)(“XXXXXX”)##(used as an object)
“Gerunds” could be “objects” of :
##color(white)(“XXX”)##…the disadvantage of overeating..
(but this doesn’t seem to be what was being asked.