"Request fulfillment" is an ITIL v3 concept. In ITIL v2, it was considered part of Incident Management. However now the two are separate: incidents are for things that are breaking or about to break, and service requests are for new things.
Request fulfillment is tightly coupled to service catalog management--request fulfillment is when services are actually ordered from the service catalog.
Request fulfillment is the process of providing "normal" services to users, such as the creation of a listserv or a Blackboard course. Request fulfillment calls these requests "service requests" because they are requests for a particular existing service. Service requests should be predictable, and popular service requests can be optimized and automated and "request models" defined for them.
Request fulfillment includes asking questions, such as "How much email quota do I have?"
Vendors try to sell request fulfillment tools, usually bundled as part of a service catalog solution. Request fulfillment and incident management are particularly linked (e.g. when a user is calling you can't be sure whether they're calling about something that's broken or something they want to order), so it is important to consider the integration needs between your request fulfillment tool and your incident management tool.
Request fulfillment often is associated with charging--if you provide a "desktop printer request" service, then people will want to order desktop printers and someone will need to pay for them. However, based on the charging model for a University IT department, it may be more difficult for IT to fund the "goods" supporting a service request. Ironically by doing a good job of request fulfillment an IT department's costs can go up.