David Flanagan answers this quite nicely in his book, JavaScript: The Definitive Guide:
The JavaScript interpreter performs automatic garbage collection for memory management. This means that a program can create objects as needed, and the programmer never needs to worry about destruction or deallocation of those objects. When an object is no longer reachable – when a program no longer has any way to refer to it – the interpreter knows it can never be used again and automatically reclaims the memory it was occupying.
This doesn't mean that memory leaks can't happen in JavaScript. Far from it. Circular (or cyclic) references are a frequent problem in browsers which implement reference counting, as documented here by IBM:
A circular reference is formed when two objects reference each other, giving each object a reference count of 1. In a purely garbage collected system, a circular reference is not a problem: If neither of the objects involved is referenced by any other object, then both are garbage collected. In a reference counting system, however, neither of the objects can be destroyed, because the reference count never reaches zero. In a hybrid system, where both garbage collection and reference counting are being used, leaks occur because the system fails to identify a circular reference. In this case, neither the DOM object nor the JavaScript object is destroyed. Listing 1 shows a circular reference between a JavaScript object and a DOM object.
If you're worried that your website contains a JavaScript memory leak, Google has a tool, aptly named "Leak Finder for JavaScript", which can help you find the cause.
Further reading: What is JavaScript garbage collection?