Tractors commonly have larger rear wheels for several reasons. One of these reasons is weight distribution. The larger the rear wheels, the further the wheel will have to sink into the ground to become stuck, which, on the common automobile, is a little over halfway between the center of the rim (wheel), and the contact point to the ground. This is the point where tires have to climb their way out increasingly more vertically, instead of pulling themselves out more horizontally.
Another reason why this is common is for ground clearance. This one's pretty simple. The further off of the ground the non functional bottom of the vehicle is, the larger objects it will be able to pass over without contact and damage.
And yet another reason for this, is incredible toque put out by a tractors transmission. You may have noticed, your little four door sedan can be more powerful than a tractor, or you may be surprised about this. It is common to think that the higher horsepower you have, the more your vehicle will be able to pull. This is not always the case. For example, my school owns a small 12.5 horsepower tractor that I have personally witnessed pull out an orange tree, roots and all. You may be wondering how so little power, can mean such high results. Well, mostly due to the low gear ratios of the tractors transmission, this is possible. As some of you may know, the larger the diameter of a circle, or the higher the circumference, the larger amount of torque the object will have due. This is due to a simple law of physics (this is also why car differentials were invented). I'll put this into terms that are easy to understand. When you spin a circle, or any shape for that matter (let's say a ruler on the end of a pencil "helicopter" style), the outside edges of that object have to spin fast than the inside of the object to keep up with the inside. The outside edge has a farther distance than the inside to cover in the same amount of time, making it spin faster and with more power. Transmissions use the same excact principle. The larger the gear is, the higher the torque. This means, in first gear in your car, you are using the largest gear in the transmission. in the highest gear in your car, you are using the smallest gear in the transmission. Wheels work the same way.
Another reason for the rear wheels being much larger than the front wheels (on the common depiction of a tractor. Not all of them) is the fact that they help with weight distribution. Commonly, the engine in a tractor will be located in the front, and anyone who's tried to pick up an engine will know, they could definitely shed a few pounds. this would cause the front of the tractor to be heavier than the back, and on many tractors, there are front attachment points. Now what happens when a baby is sitting on one end of a seesaw and a full grown obese american plops on the other side? You guessed it, bye bye baby astronaut. In other terms, the front of the tractor may tip over.