1. The practice of sifting refuse from an office or technical installation to extract confidential data, especially security-compromising information (‘dumpster’ is an Americanism for what is elsewhere called a skip). Back in AT&T's monopoly days, before paper shredders became common office equipment, phone phreaks (see phreaking) used to organize regular dumpster runs against phone company plants and offices. Discarded and damaged copies of AT&T internal manuals taught them much. The technique is still rumored to be a favorite of crackers operating against careless targets.
2. The practice of raiding the dumpsters behind buildings where producers and/or consumers of high-tech equipment are located, with the expectation (usually justified) of finding discarded but still-valuable equipment to be nursed back to health in some hacker's den. Experienced dumpster-divers not infrequently accumulate basements full of moldering (but still potentially useful) cruft.