A conjunctive adverb is used to join two simple sentences (or clauses). The following can all be used as conjunctive adverbs:
also, consequently, furthermore, however, incidentally, indeed, likewise, meanwhile, nevertheless, nonetheless and therefore
When used to join two sentences, a conjunctive adverb must be preceded by a semicolon and not a comma. (This is a common mistake - particularly with however.) Conjunctive adverbs are also known as "transitional phrases".
The instructor's English is poor; consequently, they all failed the exam.
I know Mr Evans was drunk; however, I am not responsible for his actions.
The word "however" nearly always starts a sentence. Occasionally, it can be preceded by a semicolon (when used as a conjunctive adverb). Preceding it with a comma and writing a new sentence is a very common mistake.
I normally like toffees, however, I dislike these ones.
Glossary of grammatical terms