I believe a lot less contactless credit cards in the US currently, nor are the cards I use offered as a contactless option. As such, the convenience is really twofold for me
1. Backup payment method. If I don't have my wallet, I can still pay for things. Handy for the once in a while I forget it, but more handy if I'm out for a run and want to buy a drink or something.
2. One handed operation. Since all I need to do is put my thumb on the fingerprint reader and hold my phone by the contactless reader instead of needing to open my wallet to swipe a card, it's far easier to do while trying to keep my 4yo out of the candy in the checkout line with my other hand.
Mind you these may both apply to Google Wallet as well, but I haven't used it so I can't say. Honestly, if Apple pay does nothing more than encourage the proliferation of contactless readers, I think both Apple and Android fans win.