If you are deploying to a local or remote Alfresco server, you are deploying to a new content repository (each sandbox is it's own Subversion repo, just some sandboxes share context via a Clearcase-like view mechanism called layered directories - you can read more about that on our wiki). That content repository is based on the name of your current webproject, appended with the word "live".
If you look in the node browser or in CIFS, you will see this live content repo. You can sync this live repo whether it runs on your same server machine or a remote server machine. In our upcoming 2.2 release (currently BETA), we allow you to specify the URL to your run-time site that is accessible and serving content from this live repo (our preview URLs are special-generated virtualization URLs). You can read more about this on our wiki page on Deployment.
If you are deploying to a remote file-system using our file-system receiver, you'll see all the contents of your staging snapshot on disk in whatever location you specified in your deployment config file. Of course, you'll have to have either an httpd server of some sort that maps an URL to some docroot that corresponds with this deployment target dir in order to actually see your website once deployed (once again, your httpd server and what your run-time URL is up to you).
For dynamic sites, you really need to deploy to both the file-system (deploy your code to a remote file-system, run an ant script to WAR up and deploy into whatever app server you choose) and remote repo (the live store you dynamic pages query and retrieve data from using either web scripts or our remote API). This is nice, because while we manage your entire website or web app, in the run-time, your code runs standalone on whatever app tier you what, and your Alfresco repo (unemcumbered by various authoring activities) runs as a lightweight, embedded repo services content requests from your own web app.
Let me know if more questions. And do take a look at our 2.2 deployment wiki page. Setting up and tracking these types of deployment scenarios is much simply with our new deployment config wizard.
Kevin