TCP/IP is designed for use with many different kinds of network. Unfortunately, network designers do not agree about how big packets can be. Ethernet packets can be 1500 octets long. Arpanet packets have a maximum of around 1000 octets. Some very fast networks have much larger packet sizes. At first, you might think that IP should simply settle on the smallest possible size. Unfortunately, this would cause serious performance problems. When transferring large files, big packets are far more efficient than small ones. So we want to be able to use the largest packet size possible. But we also want to be able to handle networks with small limits.
There are two provisions for this. First, TCP has the ability to "negotiate" about datagram size. When a TCP connection first opens, both ends can send the maximum datagram size they can handle. The smaller of these numbers is used for the rest of the connection. This allows two implementations that can handle big datagrams to use them, but also lets them talk to implementations that can't handle them. However this doesn't completely solve the problem. The most serious problem is that the two ends don't necessarily know about all of the steps in between. For example, when sending data between Rutgers and Berkeley, it is likely that both computers will be on Ethernets. Thus they will both be prepared to handle 1500-octet datagrams. However the connection will at some point end up going over the Arpanet. It can't handle packets of that size.
For this reason, there are provisions to split datagrams up into pieces. (This is referred to as "fragmentation".) The IP header contains fields indicating the a datagram has been split, and enough information to let the pieces be put back together. If a gateway connects an Ethernet to the Arpanet, it must be prepared to take 1500-octet Ethernet packets and split them into pieces that will fit on the Arpanet.
Furthermore, every host implementation of TCP/IP must be prepared to accept pieces and put them back together. This is referred to as "reassembly".
TCP/IP implementations differ in the approach they take to deciding on datagram size. It is fairly common for implementations to use 576-byte datagrams whenever they can't verify that the entire path is able to handle larger packets. This rather conservative strategy is used because of the number of implementations with bugs in the code to reassemble fragments. Implementors often try to avoid ever having fragmentation occur. Different implementors take different approaches to deciding when it is safe to use large datagrams. Some use them only for the local network. Others will use them for any network on the same campus. 576 bytes is a "safe" size, which every implementation must support.