I want to see owncloud files by again the owncloud server machine. Do I need tot install client program to the server machine anyway or is there any other method to reach the owncloud files in the server?
You can mount the DAV share trough davfs2 that provided a safe read/write access to files without using the owncloud desktop client (that make a useless, in this case, local copy of all files).
To do this you must install the packet davfs2 with
apt-get install davfs2
In Debian based systems, or
yum install davfs2
in RedHat Based systems.
Then you must edit the file
/etc/davfs2/secrets adding at the end a line with your login credentials, like:
And now you are able to mount the share as a normal filesystem with the
mount -t davfs owncloud.example.org/owncloud/remote.php/webdav /mnt/
More options (like permit mount to an unprivileged user) are available, owncloud doc has a good step-by-step guide to do this: https://doc.owncloud.org/server/7.0/user_manual/files/files.html#creating-webdav-mounts-on-the-linux-command-line
It's true that you can directly access your file in the data/ dir but it's not the cleanest way (especially if you want edit/add/delete them).
if you want to "take a look behind the scenes" (or haven't installed a desktop environment) you can start your file-manager and look for /var/www/owncloud/data/"username" (for the case you are running an apache-server)!