Q:

"packing with a hard knot in the pit of his stomach" meaning

... Harry Knew why she wanted to spin out their time on the riverbank; several times he saw her look up eagerly and he was sure she had deluded herself into thinking that she heard footsteps through the heavy rain, but no red-haired figure appeared between the trees. Every time Harry imitated her, looked round (for he could not help hoping a little himself) and saw nothing but rain-swept woods, another little parcel of fury exploded inside him. he could hear Ron saying "We thought you know what you were doing!", and he resumed packing with a hard knot in the pit of his stomach. 
Harry Potter and the Deathly Hallows

I don't understand "packing with a hard knot in the pit of his stomach". What does it mean?

A:

You are breaking down the sentence incorrectly. Think of it this way: "He resumed packing. While he was packing, he had a hard knot in the pit of his stomach." I think you are thinking of the packing as something that has to do with a hard knot in the pit of the stomach. It doesn't.
The sentence that immediately precedes the ones you have provided is "They packed up their things, Hermione dawdling." (Got to love google!) So, when Harry resumes packing, he goes back to packing his things, and while he is doing that he has a hard knot in the pit of his stomach.

A:

BobRodes is right on the money with his answer. Harry resumed packing. And something happened to him. He felt (or was having) "a hard knot in the pit of his stomach."
From Collins, one meaning of "knot" is the following:

If you feel a knot in your stomach, you get an uncomfortable tight feeling in your stomach, usually because you are afraid or excited.  

Generally, a knot (this particular meaning) is "an unpleasant feeling of tightness or tension in a part of the body." 

There was a knot of tension in his stomach.

From Cambridge, "the pit of your stomach" is

the center of your body, where you feel especially fear and anxiety

I got a sick feeling in the pit of my stomach before the performance.

This makes sense now. Harry, in his mind, could hear Ron saying "We thought you know what you were doing!" - {parcel of fury exploded inside him}. Harry instantly felt a knot (an uncomfortable feeling) of fear and anxiety in the pit of his stomach.

