>I need to understand (and learn) a .NET technology that would be used as follows:
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>Some 3P software has to add record(s) to a table in SQL Server database. Then my application will "deal" with this record(s) (this is not relevant to the question). I may need to "tell" the 3P software how the data from their program will go to the database. Will I need to build Web Services to consume their data/messages? (not sure if "consume" is the right term though). Or another technology?
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>What technology should I look at and learn?

Yes, a Web Service will suit well for that requirement.

You build a Web Service on the server. Then, the client can send a SOAP enveloppe which will send a hit to one of your Web Service method and you will return them a response. I always recommend to keep it simple at first. Simply return a XML string which will tell them the success of the operation with any relevant data they need to obtain from the insertion of that record in your database.