Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field.
This is correct, but the operative word here is "changing". Specifically, Faraday's law states
$$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
If you're not familiar with vector calculus, fret not! This equation basically says that the "twistiness" of the electric field is directly proportional to how quickly the magnetic field is changing. But twistiness of the electric field can set up a voltage in a conducting loop (well, technically it's an EMF, not a voltage), since a twisty electric field can push charged particles all the way around the loop.
But as I alluded to before, the problem comes from the fact that we need our magnetic field to be changing for this to happen-- if it isn't, the right hand side is zero and the electric field has no twistiness, meaning no EMF to push charges through our circuit. Now, while the Earth's magnetic field does change over time, it does so very slowly, meaning that even with a very large loop you wouldn't be able to power much.
Now, you might ask "well, the Earth might not have a field that varies quickly enough to do this, but what about other planets?" Sadly, the answer is still that it's infeasible. You see, magnetic fields have a property somewhat like inertia, in that they don't like to change. In fact, if an object has a changing magnetic field, Maxwell's equations predict that the object will act like an antenna and radiate away energy. As a consequence, most planets have relatively stable magnetic fields-- if the magnetic field is rapidly changing, it eventually slows down as energy is expended.
There are a few examples of astronomical bodies with high magnetic fields that quickly change, but they tend to be poorly suited to life and short lived. Some of the most extreme examples are magnetars, which are neutron stars with magnetic fields about 15 orders of magnitude stronger than Earth's. By virtue of having strong fields that vary quickly thanks to high rotation rates, they emit a ridiculous amount of radiation. The fields tend to decay by about 10,000 years, which is the blink of an eye by geological standards.
