Denial of Service. This attack allows an intruder to disrupt services by causing excessive processing on the target system. In order to run this attack, the hacker/cracker could execute the command:
finger rob@example.com@example.com@example.com@example.com@.....
This causes excessive CPU time by forcing the target server to recursively execute the finger until it reaches the end of the list. This is a classic style of attack that takes advantage of the situtation where it takes very little resources (CPU, network traffic) of the attackers to cause the victim to consume large amounts of resources.
A similar attack can take advantage of bouncing to also cause network traffic on the wire:
finger rob@hostA@hostB@hostA@hostB@.....
One hacker exploit script that implements a finger bomb is called "kaput".