The “second negative” is also called the “double negative.” Don’t confuse it with the “negative double” – they are totally different bids.
Partner opens 2♣
When partner opens 2♣ and you have a crummy hand, you first respond 2♦. This is just a negative bid, showing 0 to 7 points. But if you are truly dreadful, you need to turn partner off from his lofty dreams by giving him a “second negative.”
If you have zero (zippo, nada, 0000000) to 3 points, with no king (kings are good; you are bad), first bid 2♦ and then bid 3♣. The cheaper unbid minor (almost always it will be clubs) is the second negative after 2♦… it shows you are broke.
You
♠ 3 2 Partner You
♥ Q 9 8 6 2♣ 2♦
♦ 9 8 7 4 3 2♠ 3♣
♣ 9 7
Your first response, 2♦, showed 0 to 7 points. But there is a big difference between the bottom half – zero to 3 – and the top half – 4 to 7.
Your second bid, 3♣, is the second negative.