What is the purpose of Yield and how does it work?

The compiler turns this code into an enumerator. You can use this enumerator to iterate over the sequence {1, -1}:

foreach(var i in ClassName.RightAndLeft)
    Console.WriteLine(i);

results in

1
-1

Note that this property does not have two return statements and return type int. It returns an IEnumerable<int>, a sequence containing 1 and -1.

See yield keyword for more information.

One important part to note is that the second line yield return -1; is executed after the first value has been printed out by Console.WriteLine in this example.

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Since the poster is a game developer, he probably uses these two values as direction indicators and this enumeration to, well, enumerate all possible directions or something like that.