Pushing variables to Stack and Variables living in the Stack difference?

There exists one stack per thread in the JVM. Each stack is composed of several frames: each method invocation creates a new frame, and when the method invocation is done, the frame is destroyed.

Within a stack frame there are two areas :

1. The operand stack (don't confuse the word "stack" here with the JVM stack itself -- stack here denotes the area as a last-in-first-out structure).
2. An array of local variables where each variable has an index (starting at zero).

Depending on the JVM implementation, they may or may not be contiguous in memory. Logically they are two separate sections of the stack frame.

As explained in the description of aconst_null, the aconst_null instruction pushes the null object reference onto the operand stack.

And as explained in the description of astore_<n> (where n could be 0, 1, 2 or 3):

The <n> must be an index into the local variable array of the current frame (§2.6). The objectref on the top of the operand stack must be of type returnAddress or of type reference. It is popped from the operand stack, and the value of the local variable at <n> is set to objectref.

So in your example, the statement Object foo = null translates to the following:

1. Push the null (a special reference that points to "nothing") onto the top of the operand stack.

  operand stack
   __________
  |   null   | <-- null is pushed on the operand stack
  |__________|
  |          |
  |__________|
  |          |
  |__________|

2. Pop the reference from the operand stack and store it in the local variable at index 1. This local variable corresponds to foo.

  operand stack                           local variables
   __________      _______________ _______________ _______________ _______________
  |          |    |      args     |   foo (null)  |               |               |
  |__________|    |_______0_______|_______1_______|_______2_______|_______3_______|
  |          |                    store null in LV#1 
  |__________|
  |          |
  |__________|

Same steps are done for Object bar = null except that null is stored in the local variable at index 2.

Source: Java Virtual Machine Specification (See this section).