The semi-colon indicates a stronger division than a comma, but a weaker one than a full stop.
Semi-Colon with Enumerations
Use a semi-colon in enumerations if a comma is already used to further separate an item of the sequence.
Example: We have business partners in Edmonton, Canada; Waterford, Ireland; Brisbane, Australia; and Durban, South Africa.
see also: → Commas with Enumerations
Semi-Colon between Main Clauses
Use a semi-colon between two main clauses if they are not separated by and, or etc.
Example: The rain stopped; the sun came out again.
Use a semi-colon between two main clauses with conjunctions (e.g. and, or) if a comma is used in at least one of the main clauses.
Example: James had, to put it mildly, a lot of problems; and not even his best friend could help him.
Use a semi-colon between two main clauses if the second one starts with an adverb that has to be enclosed in commas (e.g. however, in fact, therefore, nevertheless, moreover, furthermore, still, instead).
Example: He didn't feel well; in fact, he had a very high temperature.
see also: → Commas between Main Clauses