Minecraft wiki entry for Defense, associated text: Delayers slow down the progress of an enemy inwards. A ring of torches is a delayer because it increases the distance mobs must spawn from the structure (and player), thus increasing the time it takes for them to reach the next layer of defense. Soul sand, slime blocks , honey blocks and slowness potion turrets are also delayers because it reduces the movement speed of anything moving on it, including mobs. Mobs avoid walking on honey blocks and prevent entities from jumping.
Obstacles are structures that mobs cannot move past without somehow overcoming them. The quintessential obstacle is a wall; a zombie cannot move past a wall without somehow creating a breach or slipping in through an unclosed door.
Damagers cause harm to an enemy, in addition to just stopping or slowing them down. They might also do neither, letting the mob through without a reduction in speed, but hitting them for damage as they pass. Currently, damagers either inflict direct hit point damage on a mob, or set them on fire. If additional status effects are added (for example, if the player can create a block, which poisons anything that moves over it, these would also fall into this category. A damaging delayer could be a moat of lava; while a damaging obstacle could be a wall of cacti.