A colon (:) is a strong punctuation symbol, and is used to indicate to the reader that some further information is going to appear in the following statement. It is usually used to: introduce a list or introduce an explanation, conclusion or amplification (this latter use of the colon gives a sense of importance to our utterance).
A semi-colon (;), instead, cannot be considered a strong punctuation symbol. In fact, its role in a sentence is more or less similar to that of a simple comma (certainly stronger than a comma, but weaker than a full stop). It can be used to: avoid to use too many commas in our sentence, separate items in a list, link sentences which are closely related together, or right before words such as however, instead, therefore.