Welcome to Honda! lol ... This is eventually going to happen to any Honda, happened to mine a couple years ago.
There is a plastic piece on the Brake Pedal that controls the Circuit for the Brake Lights. The plastic piece presses in a button (Brake Switch) and turns off the Brake Lights, however, without it there the Brake Lights stay constantly on since no pressure is on the switch (holding it down).
In your case, this plastic piece broke off, look around your driver side floor and you will see it. Honda was smart enough to make these parts out of plastic instead of metal.
Easy fix though, just stick a Bolt with Nut in place of where the plastic piece goes (small hole you see in the Brake Pedal, right in front of the Brake Switch) that is long enough to push the button down when you are not pressing the Brake Pedal. If you do this, then you will never have to worry about it again, because it wont break. If you replace it with another plastic piece it may break in the future.
