A solar eclipse occurs when the moon passes between the earth and the sun so that the sun's rays are blocked from an area on the earth. In other words, it is the shadow of the moon, on a part of the earth. There are different types of solar eclipses based on how much of the sun is blocked from the area of the earth. Even if the eclipse is total--that is, the moon completely blocks the sun--the eclipse is only visible from a small part of the earth. Sections of the earth that are near the path of totality will see only a portion of the Sun blocked by the moon, resulting in a partial eclipse.
The reason a solar eclipse can occur at all is due to the fact that the size of the moon is perfect for such an event--it is 400 times smaller than the sun, but also 400 times closer to the Earth. Due to this, when conditions are perfect the moon completely blocks the sun from view, except for the corona (plasma surrounding the sun). Because the moon's orbit is not a perfect circle, it does not always completely cover the sun when an eclipse occurs, and more of the sun is visible. These are called annular eclipses.
For more information, and pictures of the various types of solar eclipses, see the attached link.