It basically says that in return for granting the permission, if within 80 years of the deed the people next door decide they also want to build an extension they are allowed to adjoin it to the wall of your extension, remove your guttering and replace it with guttering or a valley to serve both extensions jointly, with you and them jointly responsible for maintaining the new guttering/valley.
You really shouldn't be signing something like this without taking independent legal advice you know. I don't count!!!