Question

What is the object of a gerund?

Answer 1

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).

Explanation:

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) nouns and "gerunds" are nouns.
"Gerunds" can be (grammatical) "objects" (or "subjects") 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 prepositions:
`color(white)("XXX")`...the disadvantage of overeating..
(but this doesn't seem to be what was being asked.