Chinese Astrology is heavily based in the 5 elements: Wood, Fire, Earth, Metal and Water, they come from a very ancient past and are much older than the 12 animal signs themselves.

From a practical point of view, what you need is to know their characteristics, so you can understand natal charts and the like, I will try to explain shortly all of them:

• Wood: it represents the creative forces of Nature and things that grow and get stronger, in natal charts make for strong and enterprising people, is said to provide good health and a balanced character, in the sense of being firm but also know to adapt to circumstances. It implies practical sense in whatever is done.
• Fire: it's what happen suddenly and is very intense but doesn't last very long over time, like energetic situations and people, also danger or sudden developments that require quick decisions.
  

  Fire people typically have strong personalities and you can tell that easily, also they tend to change their mind more unpredictably that others, too much often they act before they should and without meditating enough what they are doing.

  Also Fire is associated with passion and sensuality and those things, and with everything about competitions, conflicts and fights.

• Earth: Earth is special because it contains all of the other 4 elements, and appears more often on natal charts, its quality is the balance and harmony with the environment, also to be quiet and know to wait and be patient and wise.
  

  On people it has balancing qualities, although if you have too much Earth it can lead you to blocked situations that need too much time and patience. Also it implies a wisdom to know how to get things with time as your best ally, and one you get them to know how to maintain them in the long term.

• Metal: it represents cold and cutting things, everything that is efficient and functional and get its goals directly and quickly. It's the element belonging to the ming and intellectuality.
  

  People with plenty of metal in their natal chart use to be very intelligent, but also have difficulties to express their feelings and enjoy the non rational part of life; to compensate this they use to be very attractive, like having some kind of magnet to attract other people.

  It's also the element belonging to money and businesses, and everything that implies pragmatism and clear ideas.

• Water: water flows forever and never stops, is able to adapt to any shape and circumstance in such a way that overcome any obstacle without violence.
  

  It gives balance and adaptability to people, and is also related with warm and quiet feelings, with travels and sexuality.

  The excess of water makes strange unbalances that are hard to understand, at least for people not having so much water!

Note that the order is important, when Wood is burnt it produces Fire, and after a while ashes that enrich the Earth, then from Earth metal is extracted, and when melted it resembles water, and with it tools are made that can be used to cut more wood to make more fire...