Hi! I will try my best to answer you correctly.
RemoteObject permit you to instanciate object and call method
to perform action on the database. From here it's very easy to
understand the mechanism.
DataService permit you to set up a proxy, with Java or
ColdFusion, to manage the transaction with the Database and push
all changes to database on each instance of the application running
in real time.
You follow me?
By example:
In a CRM application if your manager update a client profile
behind you're in the account, you will not have to refresh the page
to see the data updated. The page will get updated by the
DataService proxy.
That's very usefull when developping application that scope
to a lot people at the same time.
That reduce traffic on the network for AJAX base application,
because there's no page of the application who perform timer base
request to query for new data, they still wait for the proxy to
update them.
Everybody get new data at the same if they're on the DB row.
And finally, it's very easy the devellop.
I wish that's help you and sorry for my english.