What is a Folio
It tells us how the printer folded his paper. The largest books were the folios, made by printing on both sides of the paper and folding the paper just once to produce two leaves with four sides of text. The paper size will vary but be approximately 12” X 15”. A quarto is where the paper is folded in half and then folded again. This will give four leaves and eight pages approximately 9.5” x 12”. The next sizes down are octavo (paper-back size), 12mo, 16mo, and 32mo.
What is the importance of a folioFor Shakespeare it provides not a definitive edition of the plays, which is no longer possible, but a scholarly production that was thought to be as close as possible to the manuscript copies of the plays.
Shakespeare wrote his plays in manuscript and probably never expected to see them in print. The manuscript was handed to the theatre producing the play. The theatre might produce a single printed and bound copy of the play for the prompter who would use it to mark stage directions, actor’s names etc. They would not sell copies of that book. Unscrupulous publishers might attend a play and attempt to write down what they heard and publish it or actors who had performed in the plays might publish their own edition. With the proliferation of these it became difficult to know exactly what Shakespeare wrote.
Contrast these two passages from Hamlet soliloquy

2nd folio: "To be, or not to be: that is the question"

Pirated Quarto
"To be or not to be. Aye, there's the point/To die to sleep, is that all? Aye all.“

That pirated quarto was published in 1603 (29 years before the folio) pub Nicholas Ling and John Trundell