A disputed flag is a flag that was issued on a post that then received an "invalid flag" flag from a user with access to moderator tools. Both the original flag and the flag used to mark it as invalid will be listed as "disputed" in the respective user's flagging summary. Once a flag has been disputed, its state will not be changed by any additional action on the post.
Additionally, an edit on a post will result in any "Very Low Quality" flags attached to it being disputed. This is because "Very Low Quality" flags are intended for posts that are unsalvageable, and an edit to the post suggests that there's a chance it could still be saved.
Disputed flags are considered neither helpful nor declined, regardless of the action taken in response to them.