magically
In a way that seems like real or pretend magic.
Magically means in a way that seems impossible or wonderful, like something out of a fantasy story. When a problem magically disappears, it vanishes so quickly and easily that it feels like magic was involved, even though you know it wasn't. When someone says their lost homework magically appeared in their backpack, they mean they found it unexpectedly, almost as if it materialized out of thin air.
In fairy tales and fantasy novels, magic means supernatural power that can make impossible things happen. Wizards in stories can magically transform objects or make themselves invisible. In real life, though, we use magically to describe things that happen in surprisingly smooth or fortunate ways.
When your mom says the dishes won't magically clean themselves, she means you actually have to wash them: wishing won't make it happen. When a musician's fingers move magically across a piano, it means their playing seems so effortless and beautiful that it's almost supernatural, even though it's really the result of years of dedicated practice.
People also use magically sarcastically when they're frustrated that something won't happen easily: “I can't magically finish my book report in five minutes!”