The most important difference between a normal function/method and a Closure is that Closures can be passed onto other functions as arguments and they serve as Callbacks to the calling function.
For example we can pass closures as arguments to methods to execute them. We can create closures ourselves, but we can also convert a method to a closure with the .& operator. And we can use the converted method just like a normal closure.
Here is the complete post on Groovy Closures