Bob-ombs are enemies in SM64. When they see Mario, their fuse lights and they start chasing him. After their fuse ends, they explode, creating an explosion object.
The bloated Bob-omb is the state when the Bob-omb gets bigger, right before exploding. Usually, this Bob-omb explodes. But if you grab it right before the explosion, it will be delayed for 12 frames. Note that if the explosion is early (by throwing the Bob-omb on the ground) It won't explode until the timer expires. The explosion is delayed, but the Bob-omb stays big, which means that its hitbox is bigger, enough to push Mario backwards.
Maintaining a Bloated State
After grabbing the bloated Bob-omb, you have to walk, then the Bob-omb will start exploding again, then you have to re-grab the Bob-omb. During these small frames of walking, you will be able to turn.
Another way of keeping it is by holding it Hands-free. You will be able to jump, jumpkick, double jump, triple jump, and ground pound. You can't turn except if you have a Wing Cap, where you will be able to fly while being pushed backwards.
Hands-free Teleported Bloated Bob-omb
If you teleport while holding a Bob-omb Hands-free, This Bob-omb will disappear. But if you go close to the first teleporter or if you teleport back, the Bob-omb will appear in front of you, giving you backwards momentum while keeping almost every movement. You can grab that Bob-omb by diving or punching. Kicking will cancel the momentum.
This trick is used frequently in the A Button Challenge, but also generally for clipping through walls, such as in the Chain Chomp's Gate clip.
Interaction with walls
The game first adds the speed to the current position and uses that point in the collision calculations. The algorithm will push the bob-omb outward from the wall if a collision occurs, so if it's already against the wall it effectively adds the component of the bob-omb's speed that's tangent to the wall. Regardless of whether a collision occurs or not, the Bob-omb's position is incremented by its speed at a later point as well. Finally, since the point used for the collision calculation is only written to the Bob-omb's position if a collision occurs, the double speed increment doesn't happen in the open field. This occurs before the Bob-omb's actual movement step, so then it moves a 2nd time before the frame ends. Thus, when Bob-ombs touch a wall, their speed is effectively doubled.
Basically, Bob-ombs always check for wall collision before moving. If they do collide with a wall hitbox, then the Bob-omb's position is incremented and pushed away by the wall.
A supersaturated Bob-omb is a Bob-omb whose fuse timer has overflowed, which vastly delays its explosion. Because the underlying glitch takes 828 days (2.3 years) to execute, it is the most time-consuming glitch in the game.