Definition: Swingweight is variously defined as "the degree to which the club balances toward the clubhead," "the ratio of the weight of the head to the grip end of the club," or, by famed clubmaker Ralph Maltby, "the measurement of a golf club's weight about a fulcrum point which is established at a specified distance from the grip end of the club."
Don't worry - it all means the same thing. And that thing is this: Swingweight is a measurement that describes how the weight of a club feels when the club is being swung.
Swingweight is expressed as a letter and number, e.g., C10 or D2. Measurements range from A0, the lightest, to G10, the heaviest. A club that is measured at D5, for example, will feel heavier when swung than a club that is measured at C7 - although both clubs' actual weight may be identical.
Swingweight is mostly used to match clubs in a set. It is ideal (although not always critical) for clubs within a set to match in swingweight.
For much more on swingweight, a more in-depth explanation is available here.
Alternate Spellings: Swing weight
Examples:
I prefer a swingweight of D1, but my friend prefers a lighter swingweight of C10.
