All the above are excellent responses to defining "business capabilities" and "business processes". For a short example as was originally asked for:
Business capability – "pay a vendor". Non-technical, not tied to particular way of achieving the capability such as a process or an application.
Business process – (often shown in a flowchart) One process to support the capability “pay a vendor” is issuing a PO, where the requester submits a request and justification to the owner of the budget to pay the PO, and the budget owner approves it and send it to accounts payable to create the paperwork and send it to the vendor, debiting her budget. The process may call out particular tools used, or may not. Process descriptions have various levels as well.