Glad you asked. Go read this and be enlightened. It includes a minimum of background about how credit cards are processed today, and why Apple Pay is different, but the real money shot is this:
Credit card security falls down because every merchant gets a copy of your credit card number, but virtually none of them really safeguard that information, so you end up with situations like the Target breach. With Apple Pay, the merchant never has your credit card number at all.
Now, some merchants are up in arms about Apple Pay because the card number isn’t the only info they don’t get — in fact, they get just about nothing, because Apple Pay doesn’t have to leak any of that demographic information at point of sale. This is a feature, not a bug, but some merchants (Rite Aid, for example) don’t see it this way because they want to use the demo data to market to you, or to sell to advertisers as an alternate revenue stream, or whatever. That’s not your problem, though.
For a consumer, Apple Pay is a slam dunk good idea. Embrace it if you can, or whenever you get a device that supports it.