Organisation owner is special account role that grants you access to have full control of your organisation. Organisation owner is only user that can see and edit "Plan and billing" options. You can see who your organisation owner is by going to
Settings > Users (Owner will be marked).
You have to be logged in as owner in order to change organisation ownership. To change go to Settings > Details. Scroll all the way down until you see "Organisation owner" option. Click on your name in the "owner" field and a list of all available users will show. By clicking on one name from the list you will confirm the action to change the current owner to the one you have selected. You will be logged out and once you login again you won't be marked as organisation owner.