The deeper you go into thaumcraft the more and more infusion you will be required to do, the problem with infusion is that the harder the infusion recipe is the more unstable the infusion becomes. If you do not stabilize the infusion altar it will fail and might not ever complete, it can also cause lightning, random explosions, taint to spawn and materials to be destroyed.
When infusing items you can see how stable the altar is by looking at the Matrix in the middle of the Altar while wearing the Goggles of Revealing:
To unlock this research you will need try an infusion recipe that is not stable and becomes very unstable during the process. This will trigger you to unlock the Infusion Stabilization Research.
You can avoid using stabilizers if you build your alter in such as way that it stays stable.
Stabilizers need to be placed the same way as candles or skulls, they can also prevent items from being knocked over or destroyed by connecting them to the pedestals with redstone relays. Pedestals also act as a relay, red rune should appear on the base.