This term is related to transmitting data over networks.
Rather than send a whole file the data is split into 'blocks' or 'packets' which are then sent separately to the destination computer.
A 'packet' contains the data itself and also other information needed to handle that data. For example the packet may contain a destination address, a source address and an error checking section.
The exact make-up of a packet depends on the protocol being used. For example Ethernet, as used in computer networks, has a very precise data packet format.