As long as they're not fully clipped, they can still fly, but they don't get a ton of lift. Parrot owners typically do it so they don't accidentally fly outside and end up in a worse situation than a few clipped feathers that grow back in a few months. Birds get spooked by the most random things, so it's hard to know what will trigger them to fly into danger

Fully clipping their flight feathers is cruel, dangerous and can result in injury when a bird falls more than a few feet. Also causes muscle atrophy and makes the birds dependant on their humans

The one I saw flew fine, for short distances and indoors at least.