I have nautilus-dropbox
installed package on my remote server.
I connect to the remote server by ssh, then run command:
dropbox start
And it starts up on my local machine, how it's possible?
Linux systems use the X11 protocol for most GUI systems.
The X11 server renders the image and accepts mouse and keyboard input.
The application acts as a client and connects to whatever X11 server you tell it to. This is done with an environment variable.
When you connect over SSH, a tunnel is created back to your local X11 server, and the shell spawned by SSH has the environment variable set to point along that tunnel to your local display.