If we look at the basic level

If we look at the basic level, then a ping packet is generally of size 56 bytes or 84 bytes (including IP header as well). However, a ping packet can also be made as large as up to 65536 bytes.
Not all computers can handle data larger than a fixed size. So, when a ping of death packet is sent from a source computer to a target machine, the ping packet gets fragmented into smaller groups of packets.
One fragment is of 8 octets size. When these packets reach the target computer, they arrive in fragments. So, the target computer reassembles the malformed packets which are received in chunks. But, the whole assembled packet causes buffer overflow at the target computer.
This buffer flow often causes the system crash making the system more vulnerable to attack.
Once the system becomes more vulnerable to attack, it allows more attacks like the injection of a trojan horse on the target machine.