To date there are two ways to buy something using the Apple Pay: physically in a store or an application that supports Apple's mobile payment system (such as the Apple Store itself, in addition to Airbnb, Best Buy, Kickstarter, Priceline, Starbucks, Uber, etc.). But, at least according to the Re / code, Apple is preparing to expand this offer to the shopping cart of online stores (via mobile sites, even).
According to sources on the site, the system works only on Safari on iOS (no Apple Pay browsing Chrome, for example) as long as the iPhone / iPad in question supports Apple Pay, of course. Apple would still be considering making the service available also on Safari on OS X. It remains to be seen how it would work on MacBooks, iMacs and the company, since Ma computers do not have Touch ID, who knows the purchase process in some way. , confirmed by the Touch ID of iPhones / iPads (we'll see what Apple is up to in this regard).
The idea would be to try to put the plan into action before the end of the year, who knows, even WWDC may not be a good stage to talk about it.