An eclipse is a lunation that happens close to one of the lunar nodes, the two points where the Moon's path crosses the Sun's. A new moon there covers the Sun; a full moon there walks into the Earth's shadow. That alignment lines up about every six months, which is why eclipses arrive in seasons, two or three at a time, rather than one by one.
The type is named the way astronomers name it: annular when the Moon is too far from us to cover the Sun completely and leaves a ring, hybrid when the same eclipse manages both along its track, penumbral when the Moon only grazes the outer part of the Earth's shadow. Magnitude is the share of the disc covered at the maximum, above 1 for a total solar eclipse and below it for a partial one; for a penumbral lunar eclipse it counts the outer shadow, because the inner one is not reached at all. Astrologers read the sign the eclipse falls in and look at charts with planets near that degree. The arithmetic here is Swiss Ephemeris. What an eclipse means for a person is interpretation, and we will not pretend it is anything else.