Several British politicians have suggested the "Norway option" as a solution to the Brexit crisis. It is also known by terms such as "Common Market 2.0" and whilst it doesn't necessarily mean joining the exact same legal framework as Norway it is worse than the current deal the UK has as part of its EU membership. Norway, Iceland and Liechtenstein are in the European Economic Area and have membership of the European Sinlge Market as a result. They generally accept full free movement of EU citizens (Liechtenstein has some exemptions but this is mainly due to its tiny size). The legal agreements defining the EEA only allow Norway et al to restrict free movement in "emergency cases" and as was found in the attempt by David Cameron to renegotiate this aspect of EU membership in early 2016, the European Commission would not accept that the UK's situation constituted an emergency.
The EU single market is defined by common rules which are defined by the EU lawmaking process which the UK, as a member state, plays a full part in with representation at all levels of the EU: Parliament, Council and Commission as well as the ECJ. The EEA member states must accept these rules to participate in the single market but they have no such representation at European level. Indeed, Norway has described their relationship as "fax democracy" and "being a good lobbyist - but a lobbyist". Norway is trapped in a relationship it cannot escape and which the UK would also be likely to encounter post-Brexit: the EU market is too large and lucrative to ignore, but to gain a significant level of access to it as a non-EU member state requires accepting laws they have little to no part in making. The Norwegians loathe this relationship but have no political or economic means of escaping it. (REFS) Norway does not participate in the customs union, which would be essential for the UK in maintaining an invisible border between Northern Ireland and the Republic of Ireland. Norway's status outside the customs union allows it a degree of freedom in setting its fishing policy but at the cost of the EU imposting import tariffs on Noreway's fish exports. The EU has been clear that the "backstop" arrangement to secure the open border in Ireland, that sees the UK participate in a barebones customs union, would require the UK to accept EU fishing regulations amongst other laws.
The Norway situation arises because of the continually unresolved conundrum of Brexit: either the UK stays close to the EU single market (and its common rulebook) or we drift away and our economy suffers, because the "trade deals" so beloved of the Brexiters rarely address non-tariff barriers - and these are far more important than tariffs when discussing modern trade, with the EU single market being the only significant international effort to address non-tariff barriers. But yet if we are to remain close to the single market to avoid harming our economy, we will end up being subject to single market laws that we no longer have a direct vote on the making of.
Both the People's Vote campaign and Best For Britain have reports explaining in more detail why Norway (or an option that closely mirrors Norway's relationship with the EU, such as the "Common Market 2.0" option bandied about by some UK politicians) is worse than the UK's existing deal with the EU and should not be considered a viable Brexit option. These reports are embedded below.