Apple Pay essentially replaces the plastic cards in your wallet and allows you to pay with your iphone or watch. If a retailer supports it then after setting it up on your phone you put your thumb on the phone and then put the phone over the reader. It is pretty quick and eliminates the bulkiness of your wallet with a bunch of cards in it.
Apple is not alone as more and more mobile payments and digital wallets are coming out. Samsung Pay, Chase Pay, etc. Wal-Mart just launched it's own Wal-Mart Pay (which I believe is only usable in Wal-Mart stores). It clearly is the future. The biggest obstacles currently are concerns over security and not all retail taking it (yet) and even if they do signage is often an issue. However, I think that as people get use to it then more and more will migrate to it and even more so as people see how much faster it is than EMV cards and you don't have to carry cards as well.
At this point, I think it is obvious that it will replace cards. As younger people replace the current population (almost half of millennials are said to have used a mobile payment app at least once) and as I said before- as people get more comfortable with it while more people have smart phones as well. Beyond that, I am not sure at this point. It would be interesting to see if a big player like Apple or Paypal or another company that likes to disrupt industries like Amazon- came in to try to replace interchange and offer lower costs and use this as the gateway to that.
On a side note, I have heard rumblings about Mastercard being a possible acquirer of Paypal. Not sure what the benefit to Mastercard would be in that though.