The famous one is the upper bound that shows that is possible to pack the 17 unit squares into a 4.6756... square. It's nice because you can draw the 17 unit squares and see how they fit.

This is about the lower bound that shows that it's imposible(?) to pack them into a 4.5058 square. It's harder to show, because there are no 17 unit squares because they can't fit because it's impossible(?). (Let's add a "(?)" for now until it ages.)

The first example is easy to understand. Green choose 16 points in a 4.4452... square and proved using geometry that any unit square must contain at least one of them. It can be printed on paper and you can cut a unit square and play with it and try to avoid all the points, that is an impossible task.

The later two are more difficult because each point has a weight, and it's harder to check visually.