You can filter out traffic meeting specific criteria in tcpdump. By default, tcpdump will capture all network activity, and you'd like to prevent it from capturing the network activity you yourself are generating by being connected to the server.
One common issue admins run into when monitoring network activity is that they have SSHed or RDPed into a machine remotely. The first n prevents hostname resolution and the second n prevents port name conversion. To prevent converting IP addresses and ports to names, you can use the -nn argument. When troubleshooting network problems, it's sometimes easier to see the IP addresses and port numbers instead.
In the first screenshot, you can see that tcpdump resolves the hosts and ports your machine is communicating with to names. For example, if I'd like to monitor and capture only 1,000 packets on the eth0 interface, I could use tcpdump -i eth0 -c 1000. This argument allows you to provide the maximum number of packets to return. One way to limit the number of packets returned is by using the -c argument. Without providing additional arguments, tcpdump will return all packets continuously. Once you know the interface you'd like to monitor (usually eth0), you can then begin monitoring packets on that interface by providing the interface name to the -i argument, for example, tcpdump -i eth0.