I don't know if someone on the C# design team came up with this term, or if it is used elsewhere in the industry. We started using it while working on implicitly typed local variables (that is "var x = whatever;") in C# 3.0. A fairly common scenario is to want the compiler to infer part of a type but be explicit about another part. For example, consider the following:
var list = new List<int>() { 10, 20, 30 };
Here the type of "list" is not given, but the type argument of the generic list is given. One imagines that this could be inferred from the initializer:
var list = new List<???>() { 10, 20, 30 };
Here the ??? means "there's a type argument that goes here; compiler, figure out what it has to be from the context".
We call this "mumble typing" because one humourously imagines the code being read as "var list equals new list of hrmhmrhrm initialized with ten, twenty, thirty."
We never implemented mumble typing, which is a bit unfortunate because it means that it is hard to make a list of anonymous type. To do so, you can use the "cast by example" trick.