^W is a control code. This specific one represents the keys ctrl+w, a keyboard command in Vi and Bash among other things. It deletes the previous word. You often see something similar with ^H as well, which is a single-character backspace. https://en.wikipedia.org/wiki/Backspace#^W_and_^U has some more information about these.

Some people use them more to make visual jokes in written text, more or less the same way you'd use strikethrough formatting in text.

…thsi typo^Ŵ^H^H…

start to appear, sometimes followed by several random letters hit in frustration, before the final hard-reset of the terminal and resignation to the fact some unsaved work has been lost.