IVs generally are important in competitive battling, as breeding for them boosts your stats in battle a little higher, and every point counts in competitive battling.
IVs boost the affected stay by 1 point each. So say you have a Pokemon with a base defense stat of 95. This leaves you with a stat of 195, or 226 with perfect IVs! That's a 31 point increase, one for each IV. With EVs and a positive nature, this makes a stat of 317, which is over 100 points over the minimum stat.
As for your Quagsire, you're missing the two IVs a specially defensive Quagsire needs most: HP and Special Defense. I would breed for another Quagsire with IVs in HP, Attack, Defense and Special Defense. If you want it to be shiny, use the Masuda Method or get a Shiny Charm to increase your chances even further.