What does "Get it in" means?

It means going all in with your chips. In this context it specifically means preflop, but it can also mean going all in at other stages of a hand. You will sometimes see it written in poker forums and chat groups as GII. You might also see the acronym AIPF, which means All In Pre Flop, and means the same here.

I think you have slightly misunderstood the video. You don't need to open tighter preflop when you are deep stacked, but you need to be less willing to get all your chips in the middle without seeing a flop.

So when you have 10 big blinds, you have to be willing to go all in with quite a lot of hands, for reasons explained in the video. At 20 big blinds you still GII quite a lot, but nowhere near as often, because you don't need to risk your tournament life as lightly as you did with 10BB.

As you get deeper stacked the effect is even greater. At 200bb at the start of a deep stacked tournament you might only want to go all in with Aces or Kings.