This backstop is something of an insurance policy in the event of the U.K. and EU failing to agree a trade deal in a 21-month transition period (which itself only happens if there is a withdrawal agreement) after Brexit. It's designed to prevent a "hard" border on the island of Ireland, and could mean Northern Ireland (which is part of the U.K.) remained closely aligned to EU rules for an indefinite period, an unpalatable prospect rejected by many politicians.
MPs also supported an amendment that states the U.K. will not leave the EU without a deal although the departure date remains the same, and the vote is not legally binding.
May said after the votes that she would return to Brussels to see if she can persuade the EU to amend the backstop part of the deal — something that both she and the EU have previously ruled out.
There has been criticism that the U.K. is just wasting precious time as the departure date draws near. Gabriel Felbermayr, the director of the Ifo Center for International Economics at the Ifo Institute, told CNBC that the votes Tuesday evening had done little to change the situation.
"We had this moment of theater again yesterday in the (House of) Commons and it was very entertaining to watch, but not very enlightening at all. We've heard the relatively negative responses out of Brussels — they are not going to renegotiate the Withdrawal Agreement — and we did not see what exactly the British Parliament really wants," he told CNBC's "Capital Connection."
"They want a technical solution to make the border in Ireland soft but what this could be is not clear so we're still at a loss. Of course, we need a compromise to make this deal possible and to avoid both sides losing economically … We do not have any further information that could calm our nerves that has come out of the British parliament yesterday."