What is Inertia Propulsion, it is a type of propulsion and it uses inertia. It almost re-uses it's energy by circling around.
This is a place with gravity so this engine cannot defy the laws of gravity, at the current time. In space there is no gravity so it can go any direction if the drive has enough motors. Some models also make a "choo choo," sound.
Here are a few quotes from a Koda's website about inertia propulsion in general meaning he does not focus on a certain drive he just explains the concept in general, he is the person who made the first picture.
"In simplified terms, inertia is the stuff you put into a ball when you throw it into the air. (The input of kinetic energy produces momentum, which has inertia.) The more inertia you put into the ball (the harder you throw it) the higher it will go. When the inertia runs out (from the resistance of gravity) the ball falls back to the ground. Isaac Newton, the father of modern science, described inertia something like this: "an object in motion will remain in motion unless acted upon by an outside force." In this case that outside force is gravity."
"Now Imagine an astronaut floating in space. If he throws a baseball in one direction his whole body moves a little bit in the opposite direction. If he had an endless supply of baseballs to throw he could propel himself through space, moving a bit faster every time he threw another ball. But that's the real problem, having to throw something away in order to go anywhere. It's how rockets work - by throwing away their fuel (very rapidly, of course, creating higher pressure at the bottom of the rocket than at the top). An inertia propulsion device would, theoretically, be able to move through space without having to throw anything away in the process."
The picture at the beginning shows the weights with the pumps going down and circling back around. Those weights are the basically two baseballs being thrown over and over without being thrown away. The baseballs not being thrown away are representing the exhaust. No baseballs being left behind is no exhaust being left behind.
It's like having a car that has no carbon monoxide output.
The dean drive
The Dean Drive is mostly meant for space exploration and travel, not a lot of on ground travel.
Here are a load of pictures of inertial engines. Related to the beginning video. The beginning video was by Steve Hampton who made these engines as well.