Delegate is an object that hold a reference to a function. Several different delegates may point to the same function. A delegate's type defines the footprint of a function it may point to.
Lambda expression is a function that doesn't have name. The only way to execute this function is to have a delegate pointing to the function. Lambda expressions are usually defined in place where you need a delegate to a function with a given footprint. This is useful to make code less verbose and at the same time more descriptive and flexible
I would suggest that you use a named function and a delegate to it whenever you have some code that is going to be called from different places. A common example is an event listener that you want to attach to several event producers.
Another point to consider writing a separate function is the complexity of the code. It isn't going to help anyone if you write a whole program inside a lambda expression.
On the other hand, you often need some trivial processing that you want to be executed in a callback manner. This is the point where you might love the lambda expressions.
What is very nice about lambda expressions that they inherit the scope they were defined in, so that you can easily your variables inside the lambda expression, and thus pass a lot of info inside. You should be careful though, see the Remarks section of
this article.
Labdas are brilliant in conjunction with LINQ.
To conclude, I have to quote yet another must-read msdn section:
When you use method-based syntax to call the Where method in the Enumerable class (as you do in LINQ to Objects and LINQ to XML) the parameter is a delegate type System.Func. A lambda expression is the most convenient way to create that delegate. When you call the same method in, for example, the System.Linq.Queryable class (as you do in LINQ to SQL) then the parameter type is an System.Linq.Expressions.Expression where Func is any Func delegates with up to sixteen input parameters. Again, a lambda expression is just a very concise way to construct that expression tree. The lambdas allow the Where calls to look similar although in fact the type of object created from the lambda is different.