The Earth casts a bigger shadow. An eclipse duration is dependent on how long it takes the Moon to move in and out of the cones depicted in the drawing. The solar eclipse requires a lot less movement of the Moon than the lunar eclipse does. read more
There is another (and perhaps more important) reason why lunar eclipses — when viewed by anyone on the night side of the Earth — last much longer than solar eclipses, due to the shadow of the moon, last only a few minutes — when viewed by someone on Earth: the Earth rotates. read more
The relative motions of the Earth and the Moon cause solar eclipses to be visible only within a strip of a few degrees in latitude, and total obscuration lasts no more than about seven minutes. Thus, at any single location on Earth, a total solar eclipse occurs only once every 300 years or so. read more
We can see lunar eclipses more readily than solar eclipses, and it has to do with proximity. The Moon is much closer to the Earth (well over 300 times closer than the Sun!), so the Earth has a much greater chance of blocking sunlight to the Moon, compared to the Moon blocking light from the Sun. read more