Immediately: Nothing.
Other than the legal advice actually being published. I don't believe a penalty has been applied. The motion refers to "Ministers" rather than named individuals.
It's a rare but well-defined process: https://publications.parliament.uk/pa/jt199899/jtselect/jtpriv/43/4310.htm points out in para 310 that it's actually been made a specific crime for the devolved assemblies, but not at Westminster.
Here's the debate from the day.
Ordinarily, this might have been a reason for resignations or the collapse of the government. In the strange post-Brexit time of incompetence, it's a Tuesday. There might be token resignations.
Long run: Nobody knows.
This makes for a bad stackexchange answer, but I'm writing this because I think it's the only reasonable one. The question of "is the government entitled to get legal advice and then keep it confidential even from the House of Commons" is one Constitutional question.
There is also the question of how negotiations carried out by the government can be controlled by Parliament: here's Bill Cash phrasing it from what I think is the pro-Brexit point of view. Given that the European Union (Withdrawal) Act 2018 is now law of the United Kingdom, is the proposed withdrawal agreement compatible with that law?
We are perhaps too accustomed to large majority well-whipped governments in which the PM tells Parliament what to do. The current situation of effectively minority government is now bringing the operation of and will of Parliament back into focus.
Leaving the EU would be a huge change to UK constitutional law on its own. The devolved assemblies are all built around the assumption of EU law applying, and so has the relationship with Ireland since 1972. This sets up a constitutional fight over devolution.
