A firewall is basically some kind of software or hardware that controls data transfers. The typical use of a firewall would be to secure the access a computer or a network of computers to another network (which may even be the internet). A hardware firewall is simply a box that is put between the local and the far network and that allows or denies transfers based on predefined rules; a software firewall is a software installed on a computer and basically does the same. It has the advantage that it can also set rules based on the software that is doing the transfer, but the disadvantage that it depends on how wise the user uses it.