In dictionary,
"would" is used to ask somebody politely to do something
Ex: Would you mind leaving us alone for a few minutes?
However, I think that explanation is so simple or it does not explain clearly.
"would" make your sentence more hesitative since it is giving a hypothesis.
And to make a sentence more polite with "would", we have to look at the real meaning of a sentence.
Ex: "Do you mind if I use your cellphone?" (the listener doesn't have to hesitate to mind it, the listener is welcome to mind it, it makes the question less forceful & therefore is more polite) is more polite than "Would you mind if I use your cellphone?" (the listener hesitates to mind it, it makes the question more forceful & therefore is less polite)
But "Would you mind leaving us alone for a few minutes?" (the listener hesitates to mind it, it makes the question less forceful & therefore is more polite) is more polite than "Do you mind leaving us alone for a few minutes?" (the listener doesn't have to hesitate to mind it, the listener is welcome to mind it, it makes the question more forceful & therefore is less polite)
"Do you mind if I use your cellphone" or "Would you mind if I use your cellphone"? Which one is more polite?