'Ping of Death' is the name given to a Denial of Service exploit that was widely used in conjunction with the Ping utility. The exploit required the transmission of an illegal packet size; that is, a packet greater than 65536 bytes. This often led to a buffer overflow on the receiving system - with sometimes disastrous and often unpredictable results: system crashes, reboots, kernel dumps and so on.
This exploit was widely used because many different platforms were susceptible, and the attacker only needed to know the system's IP address. Ping was the most common medium, but in reality the problem could be exploited by anything that sends an IP datagram - probably the most fundamental building block of the Internet.
Most platforms now have effective patches and fixes, and the exploit is no longer as dangerous as it was.