Independence from the Crown is the primary political issue in the Colonial Era of Tropico 5. Independence is supported by the revolutionaries and opposed by the royalists. The ultimate goal during the Colonial Era is to ensure that Tropico becomes independent.
In order to declare independence, a governor must have at least 51% support. This requires not only catering to the needs of the islanders (food, housing, religion, etc.) but also converting them into revolutionaries, who are naturally much more supportive of the governor's goal than the royalists.
Once the governor has the required level of support, the option to declare independence will appear by the palace. The Crown will always reject the declaration, requiring Tropico to either pay or fight for their independence. Paying gives the new nation a sovereign debt, which lowers its credit rating, while choosing to fight will cause several squads of soldiers to arrive on the island; if all the squads are defeated, the Crown will relinquish control of the island to the governor.
If a governor's mandate expires, they do not get a final chance to declare independence.