Short Answer:
Similar to how a fingerprint is a uniquely identifying characteristic of a human, fingerprint attribution is a method that attribution platforms attempt to identify a user using a combination of their device's useragent string and IP.
Long Answer:
Fingerprinting is a method that mobile measurement platforms (MMPs) like Adjust, Appsflyer, Kochava and Tune use to attribute an action to a traffic source. When a click or impression is redirected through an MMP, it is given a click ID. A click ID is a unique identifier that allows each click to be traced back to the clicks origin, and attribute the origin if any in-app activity occurs as a result of the traffic that it sent.
In a perfect world, the traffic source would also pass a Device ID (IDFA for iOS, GAID for Android), which is a unique identifier for an individual device. The combination of the unique click id and a unique device ID results in a much more accurate attribution method. Unfortunately, Device ID is only available on in-app traffic sources and can be disabled by the user if they want to limit an advertiser's ability to track them. Without the Device ID, MMPs rely on fingerprint attribution. Fingerprinting works, but it is not as accurate or as effective as Device ID attribution.