Not On Label
Private Press
Vanity Press

This is a catch all "Label" for anything that isn't on a traditional label.

There is one caveat, and that is that sometimes a privately made record would have a label but it was just one the artist created for their own records.

There isn't a set in stone definition of what a private pressed record is so this is the definition I use in regard to my collection.

A private pressed record is one that was paid for by the artist to release themselves without the help of a label.  These are sometimes called "Vanity Pressings."  These can be on a label (or imprint) named by the artist, or they can completely devoid of a label.  These records are often harder to find, and can also be of lower music quality than records released by labels.  That is, of course, subjective, but that is the general view of it. 

Here is an example of one with no label at all: Bill Swyck
Here is an example of one where the artist created their own label: Karen Kraft (KK Records)

Article on thevinylfactory.com:
https://thevinylfactory.com/features/history-of-private-press-record-releases/