There are two types of network monitors: those that monitor your own system’s network settings and those that monitor network traffic. The latter includes security tools that can also be used as hackers tools. While we don’t espouse the latter, it is worthwhile to know about these tools so you are aware of security risks to your network. A list of available tools is at Top Ubuntu Security Tools.
Netstat
Netstat is the Linux command-line tool to monitor network status and functions. There are many usage parameters. See the manual for help.
Etherape (Network monitoring)
EtherApe is a graphical utility that allows you to see (in real-time) where connections are being made on your network, or between your network (or computer) and the Internet. If you are experiencing unexpected network activity on your computer or LAN and wish to see where the activity is occurring, this is an easy tool to use. Both “local” user and “root user” installations are created; in general you must use the root user installation to see all your network traffic.
sudo apt-get install etherape