Why is the "all the world's a stage" passage in Act 3, Scene 7 of Shakespeare's As You Like It written in blank verse?
Blank verse is another term for unrhymed iambic pentameter, the very specific format Shakespeare used in most of his plays and nearly all of his sonnets. While Shakespeare also used rhyming verse and prose format in some of his plays occasionally, the overwhelming content of his dramatic writing is in this form. This famous speech in As You Like It is delivered by Jacques, an older man who is something of a fool but also a mentor figure. The speech describes the stages of a man's life, and is meant to be a moment of teaching and entertainment for those present, but also is constructed to stand alone as a memorable and self-contained monologue that has more general appeal.
This kind of passage, which fulfills a dramatic purpose but is also a somewhat philosophical exploration in its own right, and which has a more general context beyond the specific one of the scene in which it occurs, is found throughout Shakespeare's plays. A similar example, also in iambic pentameter, might be Hamlet's "To be or not to be" speech, which is not only referring to Hamlet's own specific situation, but is a generally thoughtful meditation on taking one's own life when one is unhappy. Iambic pentameter has a rhythmic flow that lends itself to dramatic modes of speech, and therefore its use in these kinds of passages lends a kind of gravitas and seriousness, even within a comedy such as As You Like It.