Actually, in Australia placing one's hand physically on a Bible and swearing an oath in a court of law are not legally required. The religious convictions of some people prevent them from doing so. A person will however be required to publicly affirm his solemn agreement to tell the truth if he objects to swearing an oath. Such an affirmation does not involve or require the use of a Bible.

It's old fashioned to do so. But it has much to do with the Christian way of thinking. They believe the book to be God himself, and in the old days, nobody would have dared to lie after putting his hand on the bible. It was never a requirement though for adherers of other religions.

They swear at bible in order to say true matters on the court.