The marks 0-9 are the last 10 files you were editing. See :h viminfo-file-marks (took me a while to find the correct help subject).
'" : the cursor position when last exiting the current buffer (:h '"). Exiting here means closing the buffer (:bd) or exiting Vim while you edit a file. It does not mean leaving the buffer (like switching to another buffer). This mark is stored in the viminfo file (see :h viminfo). It can be used to restore the cursor position when you edit the file again (see :h restore-cursor).
'^ : the position where the cursor was the last time when Insert mode was
stopped (:h '^)
'. : the position where the last change was made (:h '.).
If you insert some text, '^ and '. will point to the same location (nearly - '. is on the last inserted char, '^ after the last inserted char except for end-of-line).
If you do some change without inserting (e.g. delete a line) '. will reflect that position, while '^ is unchanged.
the cursor position when last exiting the current buffera bit more ? – David542 May 31 '20 at 05:33:bda buffer and then:ethat same file again,'"will take you to the line you were before you deleted it. If you have a viminfo file and save that mark there, that is typically used to restore the cursor to the last location whenever you open a file, so you're on the same context as when you last quit Vim on that file. – filbranden May 31 '20 at 06:15