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.
The Commons 2.0 white paper, which Brian Z raised in his answer, further asserts:
In Common Market 2.0, most EU rules would not apply to us at all as we would be outside the common agriculture, fisheries, justice, home affairs, foreign and defence policies. [...]
Finally, as members of both the Single Market and a new comprehensive customs arrangement that initially will involve applying the existing common external tariff, there would be no reason for the Irish backstop ever to be activated.
However, the white paper doesn't make clear what the customs arrangement would look like. And it's somewhat counterfactual because the UK would remain in the single market, thereby subjecting itself to EU rules and the ECJ (and the EU insisted on a number of common fisheries policies as part of the Withdrawal Agreement insofar as I can recollect).
In the same answer he also quotes Barnier, who 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 as a frictionless border option:
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.
So in other words, it's a proposal the EU might get behind, but only if the UK is basically an EU member without having any say on what the EU is up to. It only delivers Brexit in name.