We are an IDX plugin vendor that pulls MLS listing data from about 500 MLSs across the country.
Basically a CRM is "Customer Relationship Management" software - it's the piece that comes after the visitor has signed up to receive property price change or new listing update emails from the IDX solution (such as ours).
IDX and MLS basically describe the same concepts - listings online. The difference with an IDX feed is that the listing data for ALL listings in a particular MLS is available to the individual Broker or Agent. These people will create a site, add the IDX feed so that the listing data appears to be generated from their site (with appropriate listing firm and MLS disclaimers and courtesies), and then uses that info to capture clients directly through their site. This is usually done through some form of client capture (e.g., forcing a signup form on the 5th property view or something.
Hope this helps!