Any pump has two chambers. One chamber houses the motor. The other chamber is called the volute, and that's where the spinning impeller actually pushes the water. The difference is in how the motor goes about making the impeller spin, which is a trick because they are in separate chambers.
With a direct drive pump, there is a shaft that goes through the motor casing into the volute, and the impeller is attached to the end of the shaft. In submersible direct drive pumps there is a seal around that shaft, which keeps the water from coming into contact with the motor. In a mag drive or hybrid drive pump, there is no shaft. The motor creates a magnetic field that spins the impeller with no direct connection. This means that the motor casing is completely sealed.
The advantage of a direct drive pump is, because the connection is "direct", the impeller can push water at higher pressure, allowing you to pump to a greater height. There are two disadvantages though. First, the seal will eventually fail. If it is a well made German or Italian seal, it will last for years. But eventually it will fail, and your pump will have to be replaced. Also, and more importantly, a direct drive pump is much less energy efficient than a mag drive. This is because the seal has to press up hard against the spinning shaft. The motor has to expend energy to overcome that resistance, and that lowers efficiency.
While a mag drive is far more energy efficient and will typically last longer, it can't pump to nearly the same height as a direct drive pump. So if you have a low waterfall that you are pumping to, a mag drive is a reasonable option. If the water is going up 20 feet, it is probably not. Also, you will usually pay more for a mag drive pump, but if it works for you, you will easily save the extra money in energy use.
One last thing - if you want efficiency, and you want to pump to a greater height, you could consider an external pump. They are very, very efficient and are also direct drive. They are more efficient simply because the requirements of the seals are completely different. The disadvantage of an external (often called centrifugal) pump is that the setup is much more complicated.