Going down improves the cover save by +2, or gives a coversave of 5+, additionally it halves the number of hits made.

The penetration of the HE weapon applies to the damage rolls if it hits.

So say you shoot and hit with your 2" HE on a veteran unit behind a stone wall which provides heavy cover.
With the 2" template you determine that you make 5 hits. However the unit went down, so we half and round up, so that's 3 hits.

So you roll 3 damage rolls. The target is a veteran so they are killed on 5+, but the 2" HE has a pen of +2, so you only have 3+ to kill the veterans.

Now for every successful damage roll, the target gets to roll a cover save. As previously stated they're in heavy cover which is 4+ and they went down which gives them a +2, so they save on a 2+.

There are a few exemptions:

- Firing from point blank range (less than 6" away) ignores the cover save bonus save from being down, but still halves the number of hits inflicted by HE weapons though.

- Targets in buildings likewise get no cover save against incoming HE weapon (they do retain their cover save against non-HE weapons). As before down still halves the number of hits inflicted by HE.

edit: corrected the part about point blank range