Those are forms of filiation. Filiation - from filius/filia, son/daughter - was the part of a proper Roman name and in its variations a common part of indogermanic naming systems - people identified by the name of their father. F stands for filius in that context, son, N for nepos, grandson (there are further levels with pronepos for great-grandson and abnepos for great-great-grandson and so on). So in the context of your example it simply means Lucius Cornelius Scipio, son of Publius (P(ubli) F(ilius)), grandson of Publius. The filiation usually came behind the 'family name', the nomen gentile, Cornelius in this case, and before the cognomen, a kind of a nickname. So why is it abbreviated? One thing that sets the Roman naming system apart from other systems in use is that it has more parts to a name, usually three to four, canonically four in the late Republic/early Empire for men; a first name or praenomen, a family name or nomen gentile (a gens is a bit wider than a family, but it's a good analogy), a filiation using the name of the father (if you wanted to go extra legitimate, you listed your fathers father, and sometimes his father as well, as done here with Scipio and Pompeius), and sometimes a nickname or cognomen, usually inherited and used to differentiate between different branches of the same gens, f.e. the branch of the gens Iulia that had the cognomen Caesar and so were all named Iulius Caesar.

While many other cultures only used a single name together with a form of reference to the fathers name (such as Hieron, son of Agathokles or similar), the relative insignificance of the first name of Romans in the public sphere, and the additional factor that there were only a few traditional names to choose from, meant that they were usually abbreviated - so to be needlessly super correct it should say L. Cornelius P.f. P.n. Scipio, as well - and thus the first names of the father as well. Combined with the usual tendency of Roman stonemasons to abbreviate as much as they possibly could without rendering the text unreadable, meant that such common terms like f(ilius) and n(epos) were abbreviated as well. And that's what the X.F. and Y.N. do stand for. Usually, the addition of the name of the grandfather is quite rare, but it signifies a long family history and proud tradition, so you often see it with Romans from important families, or adoptees who want to assert their position.

caveat lector: in other contexts, P.F. as an abbreviation might stand for other things, such as p(ia) f(idelis), p(ius) f(elix), p(rae)f(ectus), p(ientissim-) f(ecit, -ecerunt, -aciendum) and so on, as might P.N.. Please consult with your Epigraphist or other certified ancient history specialist before using Roman abbreviations.

It stands for Publi Filio, Publi Nepoti meaning "Son of Publius, Grandson of Publius". For Lucius Cornelius Scipio, he was the son (so P.f) of Publius Cornelius Scipio Africanus. He was the grandson (P.n.) of Publius Cornelius Scipio.

Marcus Licinius Crassus was the son of Publius Licinius Crassus and the grandson of Marcus Licinius Crassus whose father's name was Publius Licinius Crassus.

You can see why they invented a shorthand way of designating which Publius we're talking about since people born 50 years apart would have the same name.

This practice is called filiation. P. F. P. N. is short for filius Publii nepos Publii, in English "son of Publius [and] grandson of Publius." (That is, both his father and grandfather were named Publius, which wasn't uncommon at all considering the rather limited pool of given names for Romans.)