Bowling pins are fat on the bottom so they won't fall over easily. Pretty obvious, don't you think?
Perhaps you're fat on the bottom too, and you don't fall over very easily.
O.K., we won't go there.
What's interesting is why being fat on the bottom makes an object stable.
That's what we're going to look at.
First of all, what's important is where most of the mass of the object is. Let's stick with bowling pins so we don't get into too much trouble, and look at where most of the mass in a bowling pin is.
Because it's wider at the bottom, the center of mass in a bowling pin is low on the object. This point (sometimes called the center of gravity) is the spot where equal mass exists on all sides. There is just as much mass above this point as there is below. It's low on the pin because the top part of the bowling pin is so narrow.
The fact that it is low is what makes the pin so hard to tip over. Here's why ...
Gravity, the force that pulls downwards, can be thought of as acting on the center of mass of the bowling pin. Gravity acts on the bowling pin to try to pull it down. As long as the pin is sitting on its base, it can't fall over, because the floor is pushing back on the base of the pin.
Even if the pin is tipped over quite a lot, the force of gravity pulling down on the center of mass is still pulling through the base of the pin, and the floor can push back on the base, preventing the pin from falling.
As long as the direction of the force of gravity on the center of mass is through the base of an object, it won't fall over.
Of course, eventually the pin will be knocked far enough over so that this force direction no longer passes through the base. When this happens, the floor no longer has a base to push back on, so the force of gravity can act unopposed on the pin, and pull it over.
The lower the center of mass, the greater the angle before it falls over.
 If we look at an extremely different situation, where a bowling pin has most of its mass near the top, and its center of gravity is high, only a very small angle of tilt will cause the force of gravity to no longer pull through the base, and the pin will tip over. Objects of this sort are not very stable.
So the location of the center of mass in an object (and how wide the base is, of course), will determine how stable an object is. Objects with a high center of gravity can be made more stable with the addition of a very wide base.
In other words, if you're top heavy, wear big shoes!
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