Lambdas bring functional programing to C#.
They are anonymous functions that can be passed as values to certain other functions. Used most in LINQ.
Here is a contrived example:
List myInts = GetAll();
IEnumerable evenNumbers = myInts.Where(x => x % 2 == 0);
Now when you foreach through evenNumbers the lamda
x=> x % 2 == 0
is then applied as a filter to myInts.
They become really useful in increasing readability to complicated algorithms that would have many nested IF conditionals and loops.