A personal wiki is a wiki kept for one person's own notes: a set of linked pages that, in Zim's words, captures the idea of a wiki "not as a webpage but as a collection of files."
The wiki began with Ward Cunningham's WikiWikiWeb, which its own history page dates to March 25, 1995. The site calls itself the first wiki and says all other wikis, including 📝Wikipedia, are descended from it; its WikiWiki page gives the name as the Hawaiian word for quick.
The VimWiki README describes it as "a personal wiki for Vim -- a number of linked text files that have their own syntax highlighting," with links written in double square brackets, a diary, and export to HTML. Zim's manual says the program "aims to bring the concept of a wiki to your desktop": every page is saved as a plain text file with wiki formatting, linking to a page that does not exist creates it, and Zim keeps track of all links so each page shows which pages link to it, making links 📝bidirectional. TiddlyWiki describes itself as "a non-linear personal web notebook."
In 📝MythOS, each idea lives as a linked memo in a library its owner holds, and every @ mention also becomes a backlink.