The nub of something is its central point or most important part. When you get to the nub of an argument, you've cut through all the extra details to reach what really matters. If your teacher says “Let's get to the nub of the problem,” she means let's focus on the heart of the issue instead of wandering around it.

The word often appears in the phrase “the nub of the matter,” meaning the essential core that everything else depends on. In a debate about whether your class should have longer recess, the nub might be whether students actually work better after more break time, not all the side arguments about what games people want to play.

The word can also mean a small lump or the stub of something. A worn-down pencil eraser might be just a nub. A tree branch broken off close to the trunk leaves behind a nub. In this sense, a nub is what's left when something has been shortened or reduced to its smallest useful form, which connects back to the first meaning: both refer to getting down to what's fundamental or what remains.