TL;DR: bi-directional memory access with some means to notify the other part about "something has changed".

It's not that different for any other PIC/E device, be it a network card or a disk/HBA/RAID controller.

If you want to understand how it came to this - look at the history of ISA, PCI/PCI-X, a short stint for AGP and finally PCI-E.

Other comments provides a good ELI15 for the topic.

A minor note about "bus" - for PCEe it is mostly a historic term, because it's a serial, P2P connection, though the process of enumerating and qurying the devices is still very akin to what you would do on some bus-based system, e.g.: SAS is a serial "bus", compared to SCSI, but still you operate with it as some "logical" bus, because it is easier for humans to grok it this way.