Folios and Quartos: Shakespeare's earliest published plays are referred to as folios or quartos according to the folding of the printed sheets and therefore the size of the book: folios being large, tall volumes and the quartos smaller and squarer.
The folio format was reserved for expensive, prestigious volumes. During Shakespeare's lifetime, stage plays were not generally taken seriously as literature and not considered worthy of being collected into folios. The plays printed while he was alive were printed as quartos.
During his lifetime 18 of Shakespeare's 38 plays were published in quartos: Othello appeared in 1622. Over half of these quartos are 'bad' ones. Shakespeare does not seem to have taken any interest in the publication of his plays, and those that did appear were often pirated. Their texts are extremely corrupt as a result of their reconstruction from memory by a member, or members, of their cast.
It was not until a few years after Shakespeare's death that Ben Jonson, a friend of Shakespeare's, defied convention by issuing a folio collection of his own plays. Not long after, some of Shakespeare's friends decided to produce a folio collection of Shakespeare's plays, and this edition is now called the First Folio.
First Folio (1623): Thirty six plays, eighteen printed for the first time, were arranged by Heming and Condell (fellow actors of Shakespeare) into sections of comedies, histories and tragedies. Because Shakespeare was already dead, he was not available to oversee the editing of the text. Many of the plays in the folio omit lines that can be found in quarto versions, and include misprints and textual corruption. The Folio is no more a definitive text than the collection of quartos.