Quoting a Guardian quick guide from today's recap on what the Commons are going to vote on:
What is the common market 2.0/Norway-plus Brexit option?
This soft Brexit compromise has been championed as a plan B for
leaving the European Union.
It is based on Norway’s relationship with the EU, which is outside the
bloc and the customs union but inside the single market. Under the
plan the UK would have to join Norway, Liechtenstein and Iceland in
the European Free Trade Association (Efta), which would then allow it
to participate in the European Economic Area (EEA).
The ‘plus’ in this option refers to a temporary customs union with the
EU, which would need to be negotiated to avoid a hard border on the
island of Ireland. This arrangement would remain in place until the EU
and UK agreed a specific trade deal.
The option has the advantage of being as close to the EU as possible
without full membership, and it would do away with the need for the
problematic backstop for Northern Ireland. Like Norway, the UK would
be outside the common fisheries and agriculture policies, and would
not be subject to the European court of justice.
But it crosses a key red line for Brexiters by continuing freedom of
movement, one of the preconditions of single market membership. It
would also limit the UK's ability to negotiate its own trade deals
while a new customs arrangement is under discussion. And it would
require continued financial contributions to the EU without an
influence inside the bloc, as the UK would no longer have MEPs or a
seat on the European Council. It also isn't entirely clear that the UK
would be welcomed into Efta.
It doesn't make clear what the customs arrangement would look like.
By contrast, Barnier was clear in the run up to May's deal in 2018, when the EU consistently rejected technological solutions, that the EU would only entertain a full Customs Union:
The only frictionless model for the future with the UK would be Norway plus, Norway being part of the Single Market plus a customs union.