First Contact
This first phase of an eclipse happens when the first small bite appears in the round shape of the sun. It appears as a fingernail chunk taken from the edge of the sun, much like a nearly full moon, and should not be watched with the naked eye. Permanent retinal damage can occur from direct observation.
Second Contact
Second contact refers to the precise moment at which the entire sun (or moon) is blacked out. This is a brief occurrence, which is observable with the naked eye. At this point, the earth is awash in a dusky light, and the sun appears to have a large black hole in the center.
Totality
This is the period of a few minutes immediately after second contact. During totality, the earth remains in a state of dusky light, while the sun appears to have a halo of light radiating outward from around the dark center. This, too, you can see with the naked eye, but only in the event of a total solar eclipse.
Third Contact
Third contact marks the time at which the sun begins to emerge from behind the moon -- or more appropriately appears to emerge from behind the moon. At this point, the moon has continued along its natural orbit long enough that it is moving out from between the earth and the sun. At this point, observation with the naked eye is dangerous and should be avoided.
Fourth Contact
This is the moment at which the sun is completely restored. There may appear to be residual effects from an eclipse. Notably, the portion of typical sunlight that normally appears as a glowing haze may continue to be blocked for a few more minutes. The entire body of the sun, however, now has an unencumbered line of sight to the earth.