Growing up in New Zealand I don’t recall the expression “a tad” being used very much at all but subsequent return visits have confirmed that it is now a firm fixture in local language.
Its origins seem to be in the US and as an abbreviation of tadpole (the baby frog), used to refer to a small child. Reference materials for British English also attribute a similar meaning.
We use it however in two main forms: as a noun
How much milk do you take in your coffee? Just a tad, not too much
And as an adverb to mean slightly,
I’m running a tad late. I’ll get there as soon as I can
Today will be a tad chilly with temperatures reaching a high of 12 degrees.
He’s a tad drunk, can’t you tell?