In my quest to understand the very odd looking \' => \' operator, I have found a good place to start, and the author is very concise and clear:
This is just the notation of C# to write down a function value. It doesn't require giving the function a name, hence this value is sometimes called an anonymous function. Other languages have other notations, but they always contain a parameter list and a body.
The original notation invented by Alonzo Church for his Lambda calculus in the 1930ies used the greek character lambda in the expression λx.t to represent a function, hence the name.