Customer groups
Segments you can target discounts at.
User guide
Segments you can target discounts at.
A customer group is a named list of customers — wholesale buyers, tea-club regulars — that a discount can target instead of naming every customer one by one. As the page itself says: "Manual segments of your customer directory. A discount can be targeted at a group instead of naming every customer."
Who can do this: groups ride the customer permissions, so the Admin manages them and directory viewers can read them. They are also a plan capability — the badge above says where they start.

New group takes a name — "Must be unique for this business" — an optional description, and the members, picked from the directory. Membership is manual and holds up to a thousand customers; there are no rule-based ("everyone who spent over X") groups. A customer can belong to any number of groups, and the directory shows each customer's group chips.
A discount's customer eligibility can name individual customers, groups, or both — a customer qualifies by appearing in either list. Retargeting a campaign then becomes editing the group, not editing the discount: add a customer to Wholesale buyers and every discount aimed at that group applies to them at their next checkout.
Deleting a group asks for confirmation and shows its member count. One thing blocks it:
Deleting a group never touches the customers in it — they simply stop being members.