Bonsai essentially means "Growing trees in a container". There are many aspects to the art of Bonsai including styling, pruning and care.
Bonsai is a Japanese word but originates from the Chinese penjing practice. See the History of Bonsai @ Wikipedia.
Bonsai Care and Techniques
Watering - The ideal amount of watering is necessary to keep your tree in good health. Trees need water daily but ensure good fast draining soils for best health.
Training - The use of wires to train branches with a desired style.
Fertilizing - Due to the small amount of soil, fertilization is necessary for nutrients. There are inorganic fertilizers and organic fertilizers available.
Re-potting - It's ideal to repot every 2-3 years to invigorate the plant through root ramification and health.