What is the purpose of XSD files?

XSD files are used to validate that XML files conform to a certain format.

In that respect they are similar to DTDs that existed before them.

The main difference between XSD and DTD is that XSD is written in XML and is considered easier to read and understand.

Without XML Schema (XSD file) an XML file is a relatively free set of elements and attributes. The XSD file defines which elements and attributes are permitted and in which order.

In general XML is a metalanguage. XSD files define specific languages within that metalanguage. For example, if your XSD file contains the definition of XHTML 1.0, then your XML file is required to fit XHTML 1.0 rather than some other format.

You mention C# in your question so it may help to think of as XSD as serving a similar role to a C# interface.

It defines what the XML should 'look like' in a similar way that an interface defines what a class should implement.