Big and large both refer to something/someone that is of a more than average size, extent or capacity.
They live in a big/large house which has 10 bedrooms and five bathrooms.
My husband comes from a big/large family. He has four brothers and two sisters.
However, big also means important:
My company organises a big event for its customers every year.
Don’t worry about arriving late. It’s no big deal. (No tiene importancia).
Big also means ‘older’:
My big brother is five years older than me.
Big and large are also used in the following expressions:
to be a big mouth = a person who is indiscreet or boastful.
to be too big for one’s boots = to be arrogant
to be larger-than-life = impressive, amazing
Think big = be ambitious