A network is two or more computers (and/or other devices) that are connected to share data, software or services.
LAN: Local Area Network
This is a network within a complex; the length is between a few meters and several kilometres
WAN: Wide Area Network
Links between systems across public communication nets
Protocol: a collection of rules for the realisation and securing of data transfers.
Devices within a network must share a protocol in order to communicate. One of the most common is the Ethernet norm.
A network card (or NIC: Network Interface Card) is an expansion card to hook a computer into a network.
Networks (not only LAN) are described through the IEEE 802 standards
A grid: a network where (potentially different kinds of) computers work together to solve a single problem. Some of the most well known are: the search for prime numbers, folding at home, SETI, but they can also be used for the hacking of encryption.