What does “if you don't mind” mean?

used to check that sb does not object to sth you want to do, or to ask sb politely to do sth

How is “if you don't mind” used?

In The Sword in the Stone (1963), one line is: “And-And now if you don't mind...”

The clip at the top of this page is from The Sword in the Stone (1963).

And-And now if you don't mind...

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