A tweet (message posted on the website Twitter) that mentions a Twitter member without using their actual username. Usually employed for negative or insulting tweets; the person you're mentioning won't see the subtweet in their Twitter timeline as it doesn't contain the @ symbol that every Twitter username has.
Someone wants to criticize a person with the username @JohnDoe on Twitter but without that person seeing the tweet in their Twitter timeline. Instead of tweeting "I think @JohnDoe is an idiot" they would subtweet "I think JohnDoe is an idiot" or "I think John Doe is an idiot". In each case the @ symbol is missing so the tweet would not appear in @JohnDoe 's Twitter timeline.