A hypercall is to a syscall what a hypervisor is to an OS. Alternatively, a hypercall is to a hypervisor what a syscall is to a kernel. A hypercall is a software trap from a domain to the hypervisor, just as a syscall is a software trap from an application to the kernel. Domains will use hypercalls to request privileged operations like updating pagetables. Like a syscall, the hypercall is synchronous, but the return path from the hypervisor to the domain uses event channels. An event channel is a queue of asynchronous notifications, and notify of the same sorts of events that interrupts notify on native hardware. When a domain with pending events in its queue is scheduled, the OS's event-callback handler is called to take appropriate action.
xen/include/public/xen.h in the Xen sources.