In linguistics, a word or phrase used to weaken the truth value of an utterance, or to use such a word or phrase. For instance, compare the sentences
"I don't think I'm going." and "I'm not going."
The former hedges the meaning of the latter. Hedges are often used to be polite, in order to soften a verbal blow to the ego or somehow diminish the message that the person being addressed isn't going to get what they want in a certain situation. (Many a semantics or pragmatics textbook will tell you that most verbal expressions of politeness come down to one of these two.)
Frequently-used hedges include: I think, I guess, maybe, perhaps, kind of, sort of, technically, somewhat, rather, and most of the modal auxiliaries (can/could, may/might, will/would, etc.) The list goes on and on: some people who can't stand the insertion of "like" and "y'know" argue that these function as hedges (though generally they don't use linguistics terminology, but rather complain that these make a speaker sound ignorant or unconfident. See people who abuse the word like for examples and discussion of this phenomenon.)
Interestingly, many hedges may at first seem to function as intensifiers (words or phrases which serve to strengthen the truth value of an utterance). Ask yourself which of the following sentences seems stronger:
"I love you." or "I really love you."
Answer (of course, language use is way subjective, but for the purposes of this exercise I'm going to pretend what I'm saying is absolute truth): "I love you." is stronger, because there's something sketchy about having to add an intensifier to a declaration of love. Or maybe I'm reading into things too much... but hey, that's why I'm a linguist.
Semanticians love hedges, because they're a semi-quantifiable sociolinguistic variable. In other words, after a bit of study, it's possible to develop a metric for evaluating the effects of a hedge, and apply predicate or fuzzy logic, and have real computational models to play with.
Hedges are often discussed in the study of language and gender. Traditionally, real men don't hedge, or at least avoid doing so like the plague. Is this a stereotype? Sure, but something rings true about it, because John Gray made his name selling tripe like this in his Mars and Venus series.