The lunar limb is like the edge of the moon - you know how when you color a shape or a picture with a crayon, you have to color all the way to the edge or there will be blank white spaces left? That's kind of what the lunar limb is like, except it's a physical edge or boundary on the moon. It's where the surface of the moon stops and the surrounding space begins.
It's called a lunar limb because "lunar" means of or relating to the moon, and "limb" means an edge or a boundary. The lunar limb can be seen from Earth when the moon is waxing or waning, which means when it's either getting bigger or smaller. When we see the moon in the sky, we usually see it as a big circle or disk shape, but if you look closely, you'll notice that the edge of the moon is kind of blurry or hazy. That's because of something called the lunar atmosphere, which is really thin and doesn't work the same way as Earth's atmosphere.
When astronauts landed on the moon during the Apollo missions in the 1960s and '70s, they actually got to stand on the lunar limb and look out into space. They saw stars and galaxies and the Earth rising in the distance. It must have been a really amazing experience! So the next time you look up at the moon, see if you can spot the lunar limb and think about all the incredible things beyond it.