Facebook needs to have some data about your preferences in order to filter effectively; the most direct interactions you can make that send this signal are liking, commenting and sharing[0]. The most directly observable result of those is that similar content to the one you "approved" will be shown much more often for some time. From my observations[1], Facebook seems to do some kind of an exponential filtering (think e^-x) - things similar (or from the same person) to those you liked will initially show up much more often, but their rate will quickly diminish. But then, if this was a good guess on Facebook's part then you're more likely to "like" some of those posts, which sustains the effect. Another example would be "forgetting curves".

It may sound crude, but it is pretty effective. They make sure that you mostly see things you're interested with, sprinkled with some other stuff - because a) you might find it important too, but they don't know, and b) everyone changes their interests from time to time.

[0] - Yes, there're options to signal "please don't show me this kind of stuff" or "don't show me stuff from this person", but I use them so rarely I don't really know if they work in any other way than just blacklisting the thing/person you pointed out.

[1] - I've noticed this directly after liking a post under a fanpage I basically never interacted with. I suddenly saw their posts everyday. Then every other day. Then every few days. Another like, and they're back to showing up daily for a while.