To edit the activities user will need to have the ability to edit activities and view the objectives in the development plan rights, these are usually the rights associated with being an administrator.
These rights can be assigned by going to edit the objective, and selecting the staff tab.
From the development plan page, select the objective with the activity you wish to edit.
Select the edit pencil next to the objective.
Once loaded go to the activities tab.
From here select the edit pencil next to the activity you wish to edit.
Make the required changes, and select save.