I found this for you: When you have a conjunctive adverb linking two independent clauses, you should use a semicolon. Some common conjunctive adverbs include moreover, nevertheless, however, otherwise, therefore, then, finally, likewise, and consequently. I needed to go for a walk and get some fresh air; also, I needed to buy milk. Reports of the damage caused by the hurricane were greatly exaggerated; indeed, the storm was not a “hurricane” at all. The students had been advised against walking alone at night; however, Cathy decided walking wasn’t dangerous if it was early in the evening. I’m not all that fond of the colors of tiger lilies; moreover, they don’t smell very good. These words sometimes show up in other parts of a sentence; therefore, the semicolon rule only applies if it helps the conjunctive adverb join two independent clauses. (See what we did there?) This conjunctive adverb rule is similar to the conjunction rule. In both cases, check that the two ideas are independent clauses that could stand on their own as sentences. If so, then you’re grammatically good to go as far as the semicolon is concerned.

Thank you for your clarification. It is highly informative.

Benjamin's answer is good. I just wanted to mention that this rule merely describes the situations where you CAN use a semicolon. It does not mean that you HAVE TO use a semicolon in these cases. If you have two clauses, and each one is independent and complete in itself, you can always use a full stop to separate them. All of the conjunction adverbs that Benjamin has listed can be used at the beginning of a sentence. (The only possible exceptions are "however" and "otherwise," which some grammar books will tell you should not be used to begin a sentence. Many people do use these words to begin sentences, particularly "however" -- including academics and professionals, in formal articles and papers.) In many cases, using a semicolon makes your sentences overly long, and therefore difficult to read. If you have a body paragraph that's divided into two parts, and each of them includes several elements, it's almost certainly better to use a full stop, even if using a semicolon would be grammatically okay. A full stop will usually make your writing more straightforward. Use semicolons in cases where you think it's very important to show that the separate clauses you're connecting are very closely related.