vty stands for Virtual Teletype. What is Teletype?

The teletype, or teleprinter, is a device used for communicating text over telegraph lines, public switched telephone network, Telex, radio, or satellite links.

Wikipedia explanation of teletype

https://en.wikipedia.org/wiki/Teleprinter

This means vty is essentially like a virtual computer screen plugged into the router that we can remotely access.

Both SSH and Telnet use this virtual monitor to let you see the router/switch.

The command

line vty 0 4

Configures 5 of these virtual teletypes (vty’s) for us to use. Can think of it having 5 monitors connected to the router. When you SSH to it, you are claiming one of these monitors. Cisco devices support up to a maximum of 16. 0-15