Bestow lets you cast certain Aura creatures for an alternative (usually higher) cost as an Aura that enchants a creature, granting it bonus stats and abilities. If that creature later leaves the battlefield, the Bestow permanent doesn't go to the graveyard—it simply becomes a regular creature on its own.
The big nuance: while attached as an Aura, it is not a creature. It can't be targeted by creature removal, doesn't count toward creature counts, and can't be blocked or attack. Only when it "falls off" does it become a creature. Also, you choose Bestow when casting—it's still cast as a spell, so it can be countered, and if the target becomes illegal on resolution, it enters as a creature instead.
In Commander, Bestow shines for resilience: your investment survives spot removal on the host, dodging two-for-ones.