A circle is a special kind of role from the supercircle's point of view. Therefore, to change the purpose of a circle, you will need to open a Governance Meeting of the supercircle. From there, you can edit the subcircle and modify the purpose.
Note: Your organization's purpose is the purpose of its largest circle. See the following link to see how to change the purpose of the organization.
In the scenario below, the circle Market Place is changing its purpose. Since Market Place is a subcircle of GCC, they will be openning a Governance meeting for the GCC circle.
Below you will see the GCC Governance meeting. A member of the GCC circle has added an agenda item and written in their tension. Now they need to select the option "Add/Edit Role".
After they have selected "Add/Edit Role" and selected the Market Place role, they can edit the purpose, highlighted in yellow below.
After editing the purpose, they select the "Accept Proposal" button at the bottom of the screen, and that's it! The purpose has been changed.