There are two types of conjunction:
- Coordinating conjunctions: There are seven in total: and, but, for, nor, or, so, and yet. They are placed between words (bacon and eggs); phrases (mad dogs and Englishmen); clauses (I know I should study more, but I just can't find the time.) and - contrary to what many of us were taught at school - sentences (I once spoke fluent Swedish. But that's another story.) of equal or similar grammatical status;
- Subordinating conjunctions, such as because, until, unless, since, if, and although, link the main clause of a sentence to a subordinate clause.
However much it may be frowned upon by some from a stylistic perspective, there is actually nothing grammatically wrong with starting a sentence with a conjunction. Michael Quinion quotes the use of that infamous initial And... (Fowler's The King’s English accepted it but stressed that it shouldn’t be followed by a comma) from the King James Bible (1611) to Lewis Carroll (in Alice in Wonderland) and Charles Dickens (in Nicholas Nickleby) both from 1865, to Harper Lee (in To Kill a Mockingbird, 1960) and Martin Amis (in London Fields, 1989).