Assuming user "username" has ssh access to server2 from server1 you can sync changes made on server1 to server2 by running this on server1:
rsync -nav /path/to/files/ username@server2:/path/to/files/
The trailing slashes are significant, see
man rsync for details.
The options used in this example are:
n = dry-run, just report what will be done without actually doing it
a = archive mode, preserves ownership details, links etc
v = be verbose
Once you are happy it is doing what you want, you can remove the n flag.
man rsync for more options, like --exclude and --delete, -z for compression may be useful too.