For more info on what DIM weight is, as well as how to calculate a specific package type, see section 1.4 of this article from USPS.
As of January 2015, you may have noticed your shipping cost increasing for UPS and FedEx. This new model of pricing is called Dimensional Weight Pricing (DIM). DIM weight is calculated based on the dimensions of the package, instead of the actual weight. If you are interested in saving money, you may want to consider using USPS as they do not use DIM Weight pricing on packages shipped domestically with Priority Mail and are under one cubic foot. Learn more with this helpful USPS video.
However, if your package is larger than one cubic foot and is not domestic, you may still run into DIM Weight Pricing.
For example: Normally, a 4 pound Priority Mail shipment, in Zone 8, is $15.52. However, this rate is based on a 12 x 12 x 12 box (one cubic foot), or smaller. Lets say that you have a box that is 14 x 14 x 14. When you ship something that is that large, USPS has what it calls a "Dimensional Weight Rule" that impacts zones 5 through 9. With the dimensions, the rate is as if the package weighed 14 pounds, not 4. This brings the cost of the shipment to $38.02.