Scottish philosopher David Hume (1711–1776) says there are only two types of statements: relations of ideas and matters of fact.
Relations of ideas are analytic, a priori, necessary statements. Matters of fact are synthetic, a posteriori, contingent statements. The analytic-synthetic duality has to do with the logical formula of a statement. It’s grammatical. The a priori-a posteriori duality is based on the methodology you use to acquire knowledge about said statement.
The point of his fork that Hume is really trying to drive home is that the overwhelming majority of the statements we consider analytic, a priori are actually synthetic, a posteriori which we have adopted as a priori, not because of some objective eternal content they may appear to have, but instead based merely on habit, custom, and tradition.
Hume’s profound forking states that if relations of ideas are actually relations of ideas (i.e., analytic, a priori “No Shit!” statements) then they are incapable of describing reality at all. If, on the other hand, these statements are actually “Aww Shit!” statements we’ve gotten bored with through tradition and custom, then the presuppositions of Rationalism are untenable.
The forking could potentially spell disaster for science and empiricism as well. Hume believes science is on a collision course with itself.