The difference between normal and half normal is the way in which the normal connection is broken.
You have two rows of jacks.
The top row is connected to bottom row. no patch chord required. This is the same for NORMAL and HALF-NORMAL.
Now if you patch into the top row with a patch chord in a NORMAL configuration, you now have the signal on the patch chord and it DOESN'T go to bottom row.
HALF NORMAL works differently..
If you patch into the TOP row with a patch chord, you have the signal on the patch chord, AND it DOES still go to the bottom row. Effectively you now have a "copy" of the signal. one goes to the bottom row. and another goes on your patch chord.
Useful for taking a split of your signal. Most times you will want a half-normal connection.