A subtweet is a tweet that talks about a person, but does not include that person's Twitter handle in the tweet. In this way, the person being talked about does not know the tweet was sent out.
When a person's Twitter handle is used in a tweet, that person receives a "mention" notification. This lets the person know that he is being talked to or about by another Twitter user. The main purpose of subtweeting is to prevent the "mention" notification from happening. Subtweeting is often used for negative purposes, such as cyberbullying, as it is a means to publicly criticize a person behind his back. The Facebook equivalent to subtweeting is vaguebooking.