declaring a variable as final helps enforce the principle of least privilege and such values might not be modified.
I think that virtual machine "works" fast in case when we declaring as final methods or/and classes due to static binding and inlining.
Virtual machine (or in fact your application) MAY run fast, it is not the case always. Most of the time it gives performance benefits because as the variable is final, it can be used for compile time optimizations of the code. For example if you are doing
range = MAX_VALUE - MIN_VALUE
where MAX_VALUE and MIN_VALUE are final variables, then this can be calculated at compile time itself and hence gives a minor performance gain. It can scale further, it such things are repeatedly, say in a loop.
If a variable is final, the JVM may choose to cache its value in a register instead of retrieving the latest value each time. If a variable is final and either a primitive or a String, then the compiler may substitute its value all over the code (like Piyush) said. Therefore, yes, it may speed up your application. However, the differences are so minute that no human will ever notice it.
Therefore, use final only if required (e.g. for anonymous classes), or if you want to indicate that a value is never allowed to change. Don't do it for performance reasons. (Although the never allowing to change is mostly enough reason, especially with instance fields.)