Crux is a big word that means the most important part of something. It's like the heart of the matter, or the thing that everything else depends on.
For example, think about building a tower out of blocks. The crux of building this tower is making sure the first block is in the right spot. If the first block is in the wrong spot, the whole tower will be crooked and might fall over. So the first block is the crux of building the tower correctly.
Another example could be making a sandwich. The crux of making a good sandwich is putting the ingredients together in the right order. If you put the bread on top of the lettuce instead of under it, the sandwich won't taste as good and may be hard to eat. So putting the ingredients together in the right order is the crux of making a good sandwich.
Basically, crux means the most important part that everything else depends on.