To be clear, from how it was worded in the direct, you get money by playing the multiplayer mode, both from your personal performance as well as a bonus for your team winning. That money is used in the various gear shops to purchase new gear (weapon sets, clothes, hats, shoes). Then there are Super Snails which are obtained by doing well during Splatfests (and I assume there will be other ways to get these, too), turned in to Spyke to adjust the perks on a piece of gear.
All of that is separate from the single player, where you use different gear (the Hero Shot and Hero Suit). It didn't look like this stuff uses the same perk system, rather the Hero gear you can level up over time by collecting power eggs (you see them scattered all around the levels and from splattering Octarians). The direct didn't seem very clear about just what leveling the gear up is supposed to do for you gameplay-wise, but I would imagine damage resistance and boosts to your ink-efficacy, etc.
