There are three different access roles that you can choose between when setting permissions on folders: Owner, Report and Initiate.
Essentially, a person or Group with Owner access can edit everything about the templates and the tasks created from them.
A person or Group with Report access can't create or edit templates, but they can view the template, all tasks created from the template, and the report.
A person or Group with Initiate access can't create or edit templates or view the report, but they can view the template and view the tasks they create from it.
All access roles can create tasks from templates inside the folder they have access to.
Where a user is represented more than once, because they are in multiple Groups mentioned or explicitly listed as a person, their access role permissions will be the highest available across those given.
What each role can and can't do in detail is listed below.
If Templates aren't located in a folder, they will be visible to all members of the organisation.