On ancient dumb terminals, it was easy to create columns of text and numbers: simply space over to the beginning of the next column.
I suspect that "column mode" has something to do with being able to select and manipulate particular columns and 2D rectangular blocks. This makes it easier to create and edit AsciiArt?. These commands are similar to the way that practically all text editors have commands for selecting and manipulating entire rows (lines, paragraphs) of text.
Right, I'd call that Rectangle or Box marking.
Now, editors such as UltraEdit, Crimson and jEdit have a true ColumnMode. In that mode, the keystrokes you type after marking a column are inserted all along the left hand edge of the column-mark. Thus, you can use it to tab/space columns over or type repeated text very quickly. It's handier than you might think.
It is also possible to do this on VIM apparently. Perhaps with an additional macro?