rsync is very good command to copy files between two linux servers.
To move a folder from server1 to server2, login to server1 with ssh
rsync -a -v --progress --timeout=0 -e "ssh -p 22" /path/to/source/folder/ user@server2-ip:/path/to/destination/folder/
Here ssh -p 22 is the default SSH port, if you use non standard ssh port, replace 22 with your ssh port number.
For example, if you want to copy (sync) folder /home/hoston/public_html/ on server 1 to server2, run
rsync -a -v --progress --timeout=0 -e "ssh -p 22" /home/hoston/public_html/ user@server2-ip:/home/hoston/public_html/
You need to run the command on the server where your files are in (source server).
rsync is not just copy, it do sync two folders, can be used for backup, so only changed files need to be transferred to remote server when you run rsync.
rsync can also used to mirror your web site to another web sever for load balancing.