In both cases you're creating a delegate with a Person parameter, returning that person's name (as a string).
In C# 6 the same syntax is used for expression-bodied members, e.g.
// Expression-bodied property
public int IsValid => name != null && id != -1;
// Expression-bodied method
public int GetHashCode() => id.GetHashCode();
delegate int del(int i);
del myDelegate = x => x * x;
int j = myDelegate(5); //j = 25
Anything before the => are the input parameters, and anything after is the expression. You can have multiple input parameters. Lambdas are mainly used with Linq.
It is part of the syntax of a lambda expression. A lambda expression is essentially a shortened form of a delegate or of an anonymous method. To illustrate, assume that I have an array of strings matching the letters of the alphabet. I could pick out the members of that array that contained values greater than "E" with the following LINQ expression:
var someLetters = alphabet.Where(l => l > "E");
The part of the lambda expression to the left of the "=>" identifies the variable name for the test (which is set to the individual members of alphabet) and the part of the lambda expression to the right of the "=>" identifies the processing. In this case the processing produces a boolean value that the Where logic uses to determine if each member of the alphabet is passed through to the someLetters array.
It's a much more concise form of method notation. The following are roughly equivalent:
// explicit method
int MyFunc(int x) {
return x;
}
// anonymous (name-less) method
// note that the method is "wrapped" up in a hidden object (Delegate) this way
// so there is a very tiny bit of overhead compared to an explicit method
// (though it's really the assignment that causes that and would also happen
// if you assigned an explicit method to a reference)
Func<int, int> MyFunc =
delegate (int x) { return x; };
// lambda expression (also anonymous)
// basically identical to anonymous method,
// except with everything inferred as much as possible, intended to be minimally verbose
Func<int, int> MyFunc =
x => x;
// and => is now also used for "expression-bodied" methods
// which let you omit the return keyword and braces if you can evaluate
// to something in one line
int MyFunc(int x) =>
x;
Think of a lambda expression as saying, "given something, return something". In the example above, the lambda expression x => x says "given x, return x", although lambda expressions don't necessarily need to return something, in which case you might read them as "given x, do something with x".
Also note that there are kind of three things called "delegate" which can be very confusing at first.
An anonymous method uses the delegate keyword, but defines a method with no name:
Func<int, int> = delegate (int x) { return x; };
Assigning a method (anonymous, explicit, or lambda) to a reference causes a hidden Delegate wrapper object to be created that is what allows the method to be referred to. (Basically a sort of "managed function pointer".)
And then, you can also declare named method signatures using the delegate keyword as well:
public delegate int TestFunc(int x, int y);
TestFunc myFunc = delegate (int x, int y) { return x + y; };
This declares a named signature TestFunc that takes two ints and returns an int, and then declares a delegate reference of that type which is then assigned an anonymous method with matching signature.