Covering the hole would bring the note down to Bb 3. With the hole covered (or no hole at all) you would get a standing wave with a wavelength of twice the length of the instrument as the fundamental pitch.
The reason for this is because the instrument is a tube capable of holding pressure in the middle, but not capable of holding pressure at either end (let's assume a flute with open ends). When you visualize a wave, remember that the wavelength is from 0, up to the highest peak, back to zero, down to the lowest peak, and back to zero again. Line two of those zeros up at either end of the tube and you now have half the wave length inside the instrument, and this is the longest wave that fits in the instrument.
When you open the hole at exactly the center, think about a wave that has 0 at either end and 0 at the hole. The longest wave capable of this has a wavelength of 1L, where L is the length of the instrument.
Basically, whatever combination of holes is open, the only notes that will resonate are ones where the wavelengths work out so the pressure nodes line up at the holes.
Now let's go back to having all the holes closed. Don't forget that you can blow harder on a flute (and more importantly, brass instruments) to raise the frequency. The only notes that will resonate are those that have nodes (0 pressure) at either end of the instrument. Since Bb3 is the fundamental pitch, you could potentially play Bb4, F5, Bb5, D6, F6, Ab6, and so on.
That's where we get into that chart on the wikipedia page. It shows A2 having a frequency of 110Hz. To get A3, we double that (220). To get A4, we need to double THAT, right? so 440. But what about 3x 110 (330)? That's where you get E4.
The "ratio within octave" means the ratio between the note given and the A below it (since that chart is based around A). So, in regards to frequency, E4 is 3x A2, but 1.5x A3. C#5 is 5x A2 (the fundamental) but 1.25x the closest A, A4. There are 1200 cents per octave (100 per note), so that column is just giving how many out of 1200 increments it is above the A below it.
That's all confusing, but think about tuning a piano. You start by tuning A440. Now you play that A440 with the A below it. If it's out of tune, the frequency won't be exactly double. If it was, the waves would line up and it would sound great. When the waves don't quite line up, you get 'beating' where the waves cycle between adding their sound together and slightly canceling each other out. You tweak the A3 until the beats stop, meaning it's at exactly 220.
You can then tune the E to that. Since E4 is 1.5x A3, the waves also line up when they're in tune. When they're out of tune, you hear the beats, and you can adjust until they line up. That's why that 1.5x is important.
Which brings us to the circle of 5ths. One you tune that E4 to A3, you can tune all the Es. And then you can tune the Bs because they're 1.5x the nearest E. Then the F#s, and so on. 12 notes later and you're back at A and you've tuned the piano. I won't get into temperament though.
Here's a great article on flute accoustics that has helpful images: https://newt.phys.unsw.edu.au/jw/fluteacoustics.html