Maybe a look at some normalling jacks will make it more clear:
There are 5 connections on a normalling jack. In order of top to bottom (for this particular one) it's High, High Normal, Low Normal, Low, Shield. In a half normal scheme you take two jumpers and tie the "High" and "Low" on the top (output) jack to the "High Normal" and "Low Normal" on the bottom (input) jack.
Now when there is nothing plugged in, these cables will be "normally" connected. If you plug into the top (output) jack the connection from top to bottom does NOT break, however you get a copy of the signal with the patch cord.
When you plug into the bottom (input) jack the "High" and "Low" connections are pushed out by the connector, removing their contact with the "Normal" connections (in purple) and breaking the "normal".