The waxing moon lasts for the first half of the moon's 29-day cycle. This is the period when the moon goes from invisible to full. During this time, water in the ground is drawn up toward the surface, and seeds absorb more water. Planting should be done during this waxing phase because it is associated with growth and fecundity, and seeds are more likely to germinate successfully. The beginning of the waxing phase is most appropriate for leafy greens such as kale and lettuce, while the end of the waxing phase is best for denser and seed-based crops such as beans, peas and tomatoes.
The waning phase of the moon is the period during which the moon changes from full back to invisible. During this period, water is moving away from the surface and plants that are started now will be less robust. The beginning of the waning period is a good planting time for root crops such as beets and carrots. The second half of the waning period is a good time for weeding and pruning, and for allowing the soil to rest a bit by engaging in other gardening chores such as dealing with compost and greenhouses.
The same general rules and moon phases that apply to planting apply to harvesting as well. Harvesting during the waxing moon will provide vegetables and herbs that are at their peak in terms of nutrition and flavor. If you harvest during the waning moon, you will be separating the produce from the plant when much of the energy is in the plant rather than the produce, where you want it.