Following this week's debate MPs will discuss amendments on the Article 50 Bill next week before a final vote in the House of Commons on 8 February.
And Davies introduced the Bill by reminding MPs of the significance of the legislation before them.
"The eyes of the nation are on this chamber as we consider this Bill," Davis said.
"For many years there's been a creeping sense in this country, and not just this country, that politicians say one thing and do another.
"We voted to give the people the chance to determine our future in a referendum, so we must honour our side of the agreement to vote to deliver on the result."
Labour's shadow Brexit secretary Keir Starmer responded by acknowledging that his party faces a difficult situation in debating legislation on Brexit, as a "fiercely internationalist" and "pro-European" party.
However, he added that as "democrats" the Labour party should not block the Prime Minister from beginning the Article 50 negotiations.
Labour leader Jeremy Corbyn is to order his MPs to vote in favour of the Article 50 Bill, but the party has seen a handful of resignations from its front bench from MPs who felt unable to support the Article 50 Bill.
Starmer added that Labour would continue to fight for greater accountability in the Brexit process, and called on the government to act "unilaterally" to protect the rights of EU nationals currently resident in the UK.
The House of Commons is expected to sit late into the night both today and tomorrow as MPs make their contributions to the debate - Conservative MPs have been told by their party whips to remain on site until midnight in case of any need for a vote in the chamber.
The government plans to trigger Article 50 by the end of March.
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