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, you're changing the purpose of the Market Place's circle. Since Market Place is a subcircle of GCC, you will be opening a Governance meeting for the GCC circle.
In the GCC Governance meeting, you added an agenda item and you select the option "Add/Edit Role".
After you have selected "Add/Edit Role" and selected the Market Place role, you can edit the purpose, highlighted in yellow below.
After editing the purpose, you will select the "Accept Proposal" button at the bottom of the screen, and that's it! The purpose has been changed.