The magnetic field the earth generates is of extreme importance. Without it, life as we know it would not exist. To see why this is, it is only necessary to understand a few basics about what causes the electro-magnetic field and what it does.
Magnetic field generator
It is believed that at the center of the earth is a core comprised of mostly nickel and iron. The core has two layers. One of these is an elastic liquid and the inner layer is solid. As the earth spins, the two layers do, too. However, the fluid portion of the core moves at a different speed than the solid part of the core. Iron, being conductive and reactive, produces electro-magnetism because of the spinning, in much the same way that dynamos operate to generate electricity for domestic consumption, just on a vastly larger scale.
Electricity and magnetism are different facets of the same thing. This means that as electricity is generated, a magnetic field forms. In the case of the earth, the field reaches well into space and surrounds the entire planet. If no other forces acted upon it, the field would probably resemble a sphere, with Earth in the center. However, there are outside forces that do act upon it, creating what would appear to be a sideways tear drop around the earth.
People are usually aware that the sun produces sunlight. This is actually a form of radiation. The sun also produces a huge amount of other radiation, across the spectrum, from radio waves to gamma radiation. As hydrogen is converted to helium, it also produces vast quantities of particles, such as photons. Collectively, the radiation and particles are normally called cosmic rays.
In general, cosmic radiation is lethal to people, plants and animals. Some are filtered by the atmosphere and are then helpful. These include infrared radiation. High energy radiation and particles, though, can be extremely destructive.
The magnetic field around the earth acts as a shield for the energetic cosmic radiation. Since most of the cosmic particles are electrically charged, and since electricity and magnetism are different faces of the same thing, the magnetic field deflects the majority of the harmful radiation away from Earth. Since it is also electrically and magnetically charged, it operates much the same way the bow of a boat does as it plows through water.
This prevents the worst of the cosmic radiation from reaching the surface of the earth. This also accounts for the sideways teardrop shape of the magnetosphere.The solar radiation creates pressure on the side nearest the sun, squishing the field toward the earth on that side and elongating it on the other side.
Some of the radiation still gets through the buffer. This represents only a tiny portion of the total, yet it is responsible for such things as sunburn.
Earth without a magnetic field As explained above, without a magnetic field, rays and particles from the sun would have little to prevent them from reaching the surface. This would kill animal and plant tissue. The atmosphere could also become so hot that it would scorch the earth. Consider that Venus has very little magnetic field. The surface temperatures there are hot enough to melt lead, though the atmospheric components are thought to be similar to the earth's, long ago.
As important as the magnetic field is, it is known that it reverses periodically, so the north pole becomes the south pole. The last time it happened, nobody was recording the event, so what happens is supposition. However, many scientists believe that when it occurs, for a brief time, the magnetic field 'winks' out. If this is true, it indicates that the earth can exist for a short time without a magnetic field.
It is known that the magnetic field of the earth is quite important, though far more complex than what has been mentioned here, and there are some good indications of what would happen without it. How important it is, however, is still conjecture. It would probably be best just to say that life as humans know it would be highly unlikely without it.