String str = null;

means a String reference, named str, not pointing to anything

String str = "";

means a String reference, named str, pointing to an actual String instance. And for that String instance, it is a zero-length String, but it is still an actual object.

Just a little update with some diagram which hopefully can help you visualize that:

assume I have

String nullStr = null;
String emptyStr = "";
String myStr = "ab";

What it conceptually is something look like:

  // String nullStr = null;

  nullStr ----------> X    pointing to nothing



  // String emptyStr = "";
                      +------------------+
  emptyStr ---------> |       String     |
                      +------------------+
                      | length = 0       |
                      | content = []     |
                      +------------------+


  // String myStr = "ab";
                      +------------------+
  myStr ------------> |       String     |
                      +------------------+
                      | length = 2       |
                      | content = [ab]   |
                      +------------------+

(of course the internal structure of the String object is not the real thing in Java, it is just for giving you an idea)

More edit for the rationale behind NULL:

In fact in some language they do not provide concept of NULL. Anyway, in Java (or similar language), Null means semantically different from "empty" object. Use String as an example, I may have a People class with a String preferedTitle attribute. A Null preferedTitle means there is NO preferred title for that people (so that we need to derive and show the title for it, maybe), while a preferedTitle being an empty string means there IS a preferred title, and that's showing nothing.

Btw, although a bit off topic: concept of Null is seen as problematic for some people (because all those extra handling it need etc). Hence some languages (e.g. Haskell) are using some other ways to handle the situation where we used to use Null.