Hello,
Most of the time a display falls off of an Apple Watch, this is due to the device's battery swelling and pushing the display out of the enclosure. (NOTE: Your battery is designed to swell that way it does not explode/catch fire. If your battery is swelling, you are not in any danger of becoming harmed by the battery as long as you do not poke it with sharp metal objects.) Apple has recently extended the Limited Warranty on the device to 3 years for swollen battery related issues.
When you bring the device in, Apple will send the device to a repair facility in your local country where it will be replaced with a new device and either sent back to the store you took it into, or send it to your residence (which ever you prefer, you have the option to choose). Because removing the swollen battery from the device could create a safety issue for the technician removing the battery; all device's with swollen batteries are replaced rather than repaired.
As long as no signs of accidental damage are found inside the device (liquid/physical damage), the repair will be at no cost to you.
Hope this helps!