This option will apply when customers trade-in an existing iPhone that they have for the iPhone XR, in which they will then have the option of paying back Apple for the phone at $18.99 a month. As it has been pointed out, this is a similar deal that Apple had offered in China, but for the US there does not seem to be any mention of an end date for this offer, but at the same time we wouldn’t wait so long to find out anyway.
Also oddly enough this deal only applies to customers who visit an Apple Store in person, meaning that you can’t do it online or send your phone in for a trade-in. It has been speculated that this is so that Apple might be able to try and convince you to upgrade to the iPhone XS or XS Max instead, or convince you to buy more accessories or even other Apple products.
Apple has been aggressively pushing the iPhone XR and it seems to be working. A recent report claimed that the iPhone XR accounted for 39% of iPhone sales for December 2018.