There are two main kinds of eclipse; solar and lunar.
Solar eclipses are when the moon gets between the earth and the sun. You can easily imagine the shadow of the moon obscuring the sun, just as the shadow of a cloud might on most days in England. As the earth rotates, the shadow moves across the earth (just as the shadow of a cloud moves when the cloud is blown along). In the middle of that shadow, the moon totally obscures the sun, that's called a total eclipse. If you move away from that place of total eclipse, you'll get to places where the moon only partially obscures the sun. That's a partial eclipse.
DO NOT look at the sun. Ever. It will damage your vision, permanently. I'd even be wary of looking at the sun using dark goggles - you'd better the absolutely certain that the goggles are dark enough. A better way is to use a pinhole solar camera and look at the image that you get.
Donald Trump looked directly at the sun during the 2017 eclipse. 'Nuff said.
Contrary to what the Times newspaper says, the shadow of the moon does not cross the sun. That's muddled thinking of a severity that makes me scratch my head.
A lunar eclipse happens when the shadow of the earth falls on to the moon. They are quite common; you get a lunar eclipse two to four times per year. It isn't as spectacular as a solar eclipse, but whereas with a solar eclipse, only the people who are in the path of the moon's shadow can see it, with a lunar eclipse, everyone on the night side of the earth can see it.
It is quite safe to look at the moon, any time you want.
Because the orbits of the earth and moon are entirely predictable, dates and times of eclipses are too.