I think one important mention here is that fragmentation happens at two levels: most commonly, an upper layer protocol message (such as an HTTP request) is fragmented into several TCP segments, each with one TCP header. Those TCP segments themselves can sometimes be fragmented into multiple IP packets if the TCP MSS (maximum segment size) is larger than the Ethernet MTU (maximum transmission unit).

IP fragmentation is typically avoided, and in IPv6 it is only allowed at the originator of a packet - if a router is trying to route an IPv6 packet larger than the MTU of the outgoing link's MTU, it must drop the packet and send a signal about the MTU back. An IPv4 router may fragment the packet, but this rarely works well in practice.