According to this answer when code uses local variables from inside lambda methods the compiler will generate extra classes that can have name such as c__DisplayClass1
You can get some insight from the C# compiler source as available from the SSCLI20 distribution, csharp/sccomp subdirectory. Searching the code for "display" gives most hits in the fncbind.cpp source code file. You'll see it used in code symbols as well as comments.
The comments strongly suggest that this was a term used internally by the team, possibly as far back as the design meetings. This is .NET 2.0 vintage code, there was not a lot of code rewriting going on yet. Just iterators and anonymous methods, both implemented in very similar ways. The term "display class" is offset from "user class" in the comments, a clear hint that they used the term to denote auto-generated classes. No strong hint why "display" was favored, I suspect that it might have something to do with these classes being visible in the metadata of the assembly.