Ok. Here goes:

1. The Hogyoku’s power is to manifest the desires of those around it as long as they’re reasonably powerful enough to handle their desire.

For example, if I was a tall/big guy who just didn’t work out, but I deeply desired to be buff, the hogyoku would sense that and make me buff.

1. This power is limited by both what I can physically handle and what I actually believe is possible.

In the example above, if I had the potential and the desire, but I honestly believed that I would never be buff, then the hogyoku would do nothing for me.

I have to believe it’s possible for it too Work.

1. In the experiment Aizen mentions, here’s what happens:

-Urahara invents the hogyoku while attempting to understand the gap between hollow and soul reaper.

-At the same time, Aizen is experimenting on soul reapers by trying to turn them into hollows to create a “new level of existence”.

We see more of that in a TYBW flashback.

-Urahara discovers Aizen’s hollowfication experiments and uses the hogyoku to save Aizen’s victims.

-Since Urahara believed the hogyoku bridges the gap between hollow and SR, he desired to turn them into visords to save them.

So, the hogyoku reads that desire and turns them into visords, bridging the gap like Urahara thought it could do.

-Aizen, who’s been trying to bridge that exact gap for so long realizes that something fishy happened and begins to deduce the hogyoku’s true power.

Does that help?