Planting by the moon has its roots in folklore and superstition, but there is actual scientific thinking to support it. The Earth is in a large gravitational field, influenced by both sun and moon. The tides are highest at the time of the new and full moon, when sun and moon are lined up with the Earth. Just as the moon pulls the tides in the oceans, so it also causes moisture to rise in the earth, and this encourages growth. Tests have shown that seeds will absorb the most water at the time of the full moon. 

In earlier times each farmer had his own planting calendar based upon moon phases. In time, these calendars evolved to allow for the various crops that were grown. It was noticed that different plants grew better when planted at different phases of the moon, and that certain crops fared better when planted when the moon was in a specific constellation. So, in addition to the moon phase, the astrological phase became relevant. 

The Moon moves through the signs of the Zodiac in the heavens every couple of days. Different signs are associated with an element of earth, air, fire or water. When the Moon is in a water sign it is the most fertile time for planting. Different types of plants have favourite signs too, leafy plants prefer the Water signs: Cancer, Pisces and Scorpio. The Earth signs, Taurus, Virgo and Capricorn are very fertile and good for planting root crops. Air signs, such as Libra, work well for flowers. As the Fire signs of Aries, Leo and Sagittarius are barren and dry, it is a good time to weed and cultivate as seeds won’t sprout. To ally the influences of the Zodiac with the actual phases of the Moon we can specify thelikely horticultural effects: 

Increased lunar gravity at the time of the New Moon causes seeds to swell and to burst. This is the ideal time to plant annual crops such as lettuce, spinach, celery, broccoli, cabbage, and cauliflower. The gravitational pull of the Second Quarter is less, but the moonlight is strong creating good leaf growth. This is a good time for planting, beans, peas, peppers and tomatoes. After the Full Moon, the gravitational pull is high, creating more moisture in the soil, but the moonlight is decreasing, putting energy into the roots. So plant root crops, beets, carrots, onions and potatoes, as well as perennials and biennials. This is the time to transplant and to prune. But with the decreased gravitational pull and moonlight of the Third Quarter, this can be your rest period.
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So, the theory is that plants sown in the correct combination of the most favourable lunar phase and sign are reputed to show increased vigour, due to having all the best influences. They are growing at an optimum rate and are not as prone to the setbacks that would affect less healthy plants. 
Can this be proved ? In 2003, Gardening Which carried out a thorough test of planting by the Moon, using the lunar sowing calendar. The tests showed no difference at all in the yield of various vegetables sown on “good” days or “bad” days. But even though there is no proof, if you have the gut feeling that this might be worthwhile – go ahead and try it, and for luck you might like to hum - “ By the light of the silvery moon”.                  
Paul Balen - 2013