(v) To have a specific functionality. For example, a word processor that supports graphics is one that has a graphics component. The word support, however, is vague. It could mean that the word processor enables you to create graphics illustrations, that you can insert graphics created by another program, or something entirely different.
(n) Short for customer support, the assistance that a vendor offers to customers. Support can vary widely, from nothing at all to a phone hotline to house calls.