This is a very useful auxiliary verb that adds mood to your use of the language.
It’s the past tense of will
.See the cloud below
She said she would meet us next week.
Past with would have
He would have gone if he had time
He would rather stay than go back to his country.
Would you bring me my coat on your way to work?
Preference, when you want to show preference of something over the other.
E.g I would rather take coffee than tea.
I wouldn’t like to see it snow in early spring.
See word cloud below that shows would’s functions