The word "squeeze" can be used in a few different ways:
If you "squeeze" something, it just means that you push on it on both sides to make it a little smaller (at least for a short period of time). For example:
When you shake hands with someone, you're supposed to squeeze firmly, but not too tightly.
Another way to use "squeeze" is "squeeze in (somewhere)". This means to fit yourself into a place that's really small and tight. For example, if you have 3 people already in the back seat of a taxi, you can say:
Can I squeeze in between you guys?
In the example at top, the speaker says "squeeze ___ in ___". This is used when you're putting something into a tight place:
I think I'll be able to squeeze everything all in one bag.
You can also talk about "squeezing" something into someone's schedule:
Hi Patricia, could you squeeze me in this afternoon?