"It's a big silver ball; it gives us answers to things." -The Middleman
In technical terms, the High Energy Yield Data Accumulation Resource (referred to almost exclusively as the "HEYDAR") is a "global analysis and information gathering device capable of performing onboard evidence analysis as well as universal intelligence searches across all data platforms". It is located in the center of Ops in Middleman Headquarters.
It can be connected directly into Ida, or it can be used by the Middleman directly. Its processing capabilities are extreme, accessing any databank on any computer system the world over. It is also armed with a variety of weapons and destructive devices, including a shrink ray (and the reverse), a particle accelerator, and a switch which can initiate a self-destruct sequence for Middleman HQ.
The HEYDAR is a device only the Middleman is supposed to have, but at least one other is known exist. It was made by the Clotharian special forces agent Cindy Marshall, and used to attack the Middle Organization's HEYDAR online. After Cindy's death, the Middleman and Wendy Watson took Cindy's smaller HEYDAR (which they nicknamed "Baby HEYDAR") back to HQ to serve as a backup.