We're putting unit squares into larger squares, without letting them overlap. Say you want to put 5 unit squares in a bigger square. You could put them into a square of side length 12, or 100, or 3, with various arrangements. This page is showing the smallest known square that you could put n squares into, for each value of n, along with how they need to be arranged to be able to achieve that.
I believe what it means is: shown below are, for each n, the smallest square that fits n unit squares inside it. N is not shown if the smallest square that fits n unit squares inside it has no tilted unit squares inside it [except that's obviously not quite true, plenty of no-tilted-unit-square squares are shown].
from context I am guessing that the non-tilted ones that are shown are provably the smallest possible such squares, not just the smallest known. But that is not stated explicitly.
