A simple example is you are talking to a few friends on WhatsApp about booking a holiday somewhere, you talk about locations, dates, prices, etc. all in private, now Facebook can take all that data and using their massive Facebook tracking system start advertising offers for hotels in the places you are looking at going, shops you often mention that sell clothes for your holiday, travel insurance, etc, etc.
You don't need to stick ads IN the app to monetise it. In fact keeping it clean and ad free is the best thing to do as it keeps your users happy and using your app more which in turn leads to more and more data collection.
I think the $1 a year thing is a load of crap that is used to distract people away from the whole "if it is free you are the product" idea. If WhatsApp looks like it is not free because you have to pay $1 a year then psychologically you "trust" it more because it is something you pay for rather than something that is analysing every thing you ever say to build a better advertising profile. Also has anyone actually ever paid that $1? I don't know anyone who has, they always get some "promotion" that gives them another year free for being a loyal WhatsApp user.