First, the reason why this is a good question is because without stable temperatures, there is little chance of having the abundance of life that we have today. Even with ice ages, when much of the Earth is covered with huge ice sheets, life has been able to survive.
(1) One factor that contributes to Earth's stable temperatures is the existence of an atmosphere. Even though it is very thin, the atmosphere is like a "blanket" around the Earth that traps heat energy from the Sun. When sunlight reaches Earth, some of it is reflected back out into space, but most of it is absorbed by Earth's atmosphere, land, and oceans. When this energy is re-radiated back into the atmosphere, again, some of it is absorbed by the atmosphere.
To understand the importance of an atmosphere, consider a planet like Mercury, which has virtually no atmosphere. The side of Mercury that faces the Sun is very hot while the side that faces away is very cold. In contrast, on Earth, the temperature is relatively stable. Think about the difference in temperatuare between day and night. It may be as little as 30 degrees F difference. However, on a planet like Mercury, the difference can be in the hundreds of degrees F.
(2) Another factor is the existence of Earth's oceans. As you may know, the oceans cover roughly 70% of Earth's surface. Like the atmosphere, the oceans also absorb light energy from the Sun. Because the oceans are fluid and because of special propertie of water, oceans are able to "hold" onto this heat energy. If you have studied weather, you may know that the temperatures of locations near large bodies of water (e.g., the west coast of California) are moderated because during daytime water absorbs heat and during nighttime water releases this energy slowly into the surroundings, helping to keep the temperatures from dropping too low. For example, consider a desert. In the daytime, it is very hot, and, at night, it is very cold. Land is not able to hold onto heat energy.
(3) Another factor is Earth's rotation. Because Earth has a relatively fast rate of rotation (it takes 24 hours for one rotation), the fluid materials on Earth's surface (i.e., atmosphere and oceans) move. By moving, these materials mix hot and cold, helping to keep temperatures moderate and stable. For example, consider the Gulf Stream, an ocean current that originates at the equator, flows north along the East Coast of the U.S., and eventually ends in Europe. The Gulf Stream is very important because it brings warm water from the tropics to Europe. If the Gulf Stream did not exist, Europe would probably be too cold to grow crops.
(4) Another factor is Earth's orbit around the Sun. The shape of the orbit is elliptical (i.e., oval), but it is nearly circular. So, as Earth orbits the Sun, it receives basically the same amount of energy all year. The reason why there are seasons in the Northern and Southern Hemispheres (not at the equator) are due to Earth's tilt.