The government wanted to use something called the royal prerogative to trigger Article 50 to start the process of leaving the EU. Royal prerogative is kinda complicated, but it basically serves as the raison d'etre for many of the government's executive actions. It is acknowledged that parliament is supreme in the UK, so the current government is trying an end run around that long-established fact, and will dilute the power of parliament if it gets its way.
Also, the entry into the EU was done via acts of parliament, so to use the royal prerogative to just nullify those laws at a stroke would set a terrible, possibly disastrous precedent. By curtailing the use of the prerogative the court struck a blow for democracy against a power grab by the government. So it's actually a great day for democracy in the UK.
One more thing: the referendum was non-binding, so yes, it's legitimate to not be bound by it.
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