UK Parliament passed a law recently in an attempt to block a no-deal Brexit.
Government representatives keep saying that the PM will "test the law".
Which seems to be different from "breaking the law". What does it actually mean?
In common law jurisdictions, the judiciary does not give opinions on whether a bill proposed or an act passed by the legislature is legal or not - they decide controversies that arise under those acts.
The executive is obliged to follow the law so if they do something the law prohibits or don’t do something the law requires then someone with standing (usually someone affected by that act or omission) can take them to court and seek an order for them to stop (an injunction) or to do what they are required to do (a writ of mandamus).
In the present situation, it’s my understanding (and I may be wrong) that Parliament has enacted a law that requires the Executive (in the person of the relevant Minister of the Crown) to request an extension from the EU if Parliament has not approved a Brexit deal. Testing the law would mean the Minister not doing that or stating an intention not to do it. A person with standing can then petition the court for a writ of mandamus requiring the Minister to do it. If the Minister still refuses they would be in contempt and subject to being gaoled until they did.
"Testing the law" is a polite, British way of saying strategically breaking the law in order to bring the issue to court where the merits can be decided in order to establish case law.
It probably means 'find out what the law actually directs, and whether it can be sustained under judicial scrutiny'. Given the political and legal confusion that has surrounded Brexit for the last couple of years, this is as likely to work as everything else that has been tried - i.e. not very.