Welcome to LQ!
It is an archive of LVM2 configurations observed on the system.
The files present tend to be N-2 and older versions of the LVM-MetaData for a given VolumeGroup.
When you run an lvm command that will change the layout of the PV/VG/LV and, subsequently, the metadata, the backup copy of the VG is transitioned from /etc/lvm/backup/VGname to /etc/lvm/archive/VGname_#####.vg, the on-disk metadata is then copied to /etc/lvm/backup/VGname and the on-disk metadata is updated with the command executed. There is a little more that goes on, but that's the gist of it.
It provides a historical reference for the LVM2 configuration(s) known to the system. The files are plain-text and may be viewed with common editors (vi, nano, emacs) or pagers (less, more, cat). The information contained within the files is that of the LVM2 VolumeGroup's layout at the time the file was generated.