A semi-colon is a very useful grammatical device that allows a writer to connect their ideas together in a dramatic fashion. The SLC on Chico State's campus has in-depth handouts describing semi-colon use. I'll provide just some general ideas. First, a semi-colon is used to connect two independent clauses. This means that they are sentences which could be left in a sentence by themselves. Next, semi-colon's are generally used to take two independent ideas and show their relation. Here's an example.
Let's say I want to connect the two independent ideas expressed in these sentences: "I enjoy writing and do it all the time," and "Writing for me is very time consuming." I could write them with just a conjunction: "I enjoy writing and do it all the time, but this is very time consuming." But if I use a semi-colon, it might come out like this: "I enjoy writing and do it all the time; however, this is very time consuming." The advantage of the later sentence is it clarifies the ambiguity in the first sentence. The first one has two conjunctions, making it read, "This and this but this." The second one makes it clear that the conjunction 'and' has a scope confined to the first part only, and the 'however' makes connection by the second much more clear and impacting. It shows that the second sentence is a qualification of the entire part of the first.
When using semi-colons, until you become comfortable with them, it is always advisable to use 'semi-colon words,' such as 'however,' 'moreover,' etc.