The word "vast" means "really big". But "vast" is not a really common word. It's mostly used in a few situations and phrases:
Use it when talking about outer space.
The distance between us and the nearest star is so vast, it takes about 4 years for its light to reach us.
Use it with the word "difference":
There's a vast difference between playing with someone else's kids and having kids of your own.
- Use it with the word "majority":
The vast majority of people in the world have never even ridden in an airplane, much less a private jet.