Red Doors are, obviously, doors. In the City of Glass, however, most regular doors cannot be opened or passed through. Only Red Doors can be passed through by means of attacking. Punching, ramming, kicking of any kind, and even shooting these doors would make them open.
These doors separate rooms and from an interior of a building to the outside world. Please note that these doors would not open from the other side. Plus they close automatically after a few seconds after being opened. However some doors break, making them stay open permanently until the player dies or the player restarts the level.