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.