All data going to and from a computer over the network to which it is connected travels in packets. (We are assuming TCP/IP, UDP/IP, ICMP, etc. here.) This includes remote-shell connection, file-transfer, Web-related activity... Most (all?) Unix-like operating systems can filter can filter these packets against administrator-configured ordered lists of rules to help prevent unwanted connections, DOS attacks and (dramatically) improve security.
Below we consider
Quoting Wikip[a]edia:
...a stateful firewall is a firewall that keeps track of the state of
network connections (such as TCP streams, UDP communication) traveling
across it. The firewall is programmed to distinguish legitimate packets
for different types of connections. Only packets matching a known
connection state will be allowed by the firewall; others will be rejected.
For example: if a new connection is made from the outside into a system, and the associated packet is accepted by the stateful firewall, associated incoming and outgoing packets may be automatically accepted without the need to code additional rules.
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