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That's a cool question, and it has a cool answer.
It all has to do with sizes and distances. The moon is about 240,000 miles from the earth. That sounds like a long distance for sure. But relatively speaking, the moon is a lot closer to the earth than it is to the sun... almost 400 times closer. Because of this relative closeness, when the earth (which also is a lot bigger than the moon) comes between the sun and the moon, the shadow of the earth (which causes an eclipse) has a pretty good chance, each month when there's a full moon, of blocking out the moon. Conversely, a relatively small moon 240,000 miles away from the earth has a much smaller chance of blocking out a very distant (and apparently small) sun which, in the sky, as seen from the earth, looks almost excatly the same size as the moon.
Although not drawn to scale, the link below may help you understand the relationships better.
Actually, if you consider partial as well as total eclipses, it is not true that there are more lunar eclipses than solar eclipses. The number of both is very close.
In his classic book More Mathematical Astronomical Morsels, the famous Belgium astronomer Jean Meeus reported that there were 228 solar eclipses and 229 lunar eclipses in the 20th century, from the years 1901 to 2000.
For the years 1 to 3000, Jean Meeus figures there are 7,124 solar eclipses and 7,245 lunar eclipses.
And for the 5,000-year period from 2000 B.C. to A.D. 3000, NASA’s Fred Espenak – sometimes known as “Mr. Eclipse” – finds 11,847 solar and 12,186 lunar eclipses.
What you say, that the number of solar eclipses is less than the number of lunar eclipses is true if only total eclipses are considered. This will follow from the excellent explanation provided in the earlier response. The size of the Earth and that of the Moon and the distance between the Earth and the Moon and that between the Earth and the Sun, explains why total lunar eclipses outnumber total solar eclipses.
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