The most important reason of a String being made immutable in Java is Security consideration. Next would be Caching.
I believe other reasons given here, such as efficiency, concurrency, design and string pool follows from the fact that String in made immutable. For eg. String Pool could be created because String was immutable and not the other way around.
Check Gosling interview transcript here
From a strategic point of view, they tend to more often be trouble free. And there are usually things you can do with immutables that you can't do with mutable things, such as cache the result. If you pass a string to a file open method, or if you pass a string to a constructor for a label in a user interface, in some APIs (like in lots of the Windows APIs) you pass in an array of characters. The receiver of that object really has to copy it, because they don't know anything about the storage lifetime of it. And they don't know what's happening to the object, whether it is being changed under their feet.
You end up getting almost forced to replicate the object because you don't know whether or not you get to own it. And one of the nice things about immutable objects is that the answer is, "Yeah, of course you do." Because the question of ownership, who has the right to change it, doesn't exist.
One of the things that forced Strings to be immutable was security. You have a file open method. You pass a String to it. And then it's doing all kind of authentication checks before it gets around to doing the OS call. If you manage to do something that effectively mutated the String, after the security check and before the OS call, then boom, you're in. But Strings are immutable, so that kind of attack doesn't work. That precise example is what really demanded that Strings be immutable