I see now that 8.04 is using GVFS. Could someone explain what it is in
layman's terms?

GVFS is the new GNOME Virtual File System, a replacement for a previous component named GnomeVFS. A virtual file system lets you access your disks (file:// in a GNOME application) but also things like gphoto2:// for cameras and smb:// or ftp:// for network files. Applications use the VFS API and gain the ability to read and write files on any device supported by the VFS.

One of the specific advantages of GVFS is support for FUSE (too many acronyms yet?), the "userspace file system" which lets you connect to other file systems like NTFS (Windows) and ZFS (Solaris) without needing kernel drivers. This is of particular note for ZFS, Sun's new all-singing-all-dancing storage management and file system. Licensing incompatibility between Sun's CDDL and Linux's GPL means that while ZFS is "open source", it cannot be implemented in Linux. FreeBSD does not have this restriction and ZFS is available in 7.0-RELEASE.

There is also a similar component of KDE named KIO.

The GNOME 2.22 release notes provide a brief introduction: http://library.gnome.org/misc/release-notes/2.22/#sect:gvfs

Also, why is my home directory now no longer on
/dev/hda4 (which is where /home was located before), and instead what
seems to be a virtual file system on /dev/hda3 (the / partition).

Filesystem 1M-blocks Used Available Use% Mounted on
/dev/hda3 23651M 6418M 16042M 29% /
/dev/hda4 47956M 22185M 23335M 49% /media/disk

What do you see on /media/disk? What makes you think that /dev/hda3 is virtual?

Also, I can no longer move files/folders to the Trash
from hda4 -- I can only delete them permanently. Is there a reason for
this, and is it possible to enable sending to Trash for this partition?