eight-immortals:

The Wu Xing (Chinese: 五行; pinyin: Wǔ Xíng), also known as the Five Elements or Five Phases, is one of the major systems of thought within traditional Chinese fields including Chinese medicine, Feng Shui, Astrology, Music, Military Strategy and Martial arts.

A Short History
The Wu Xing theory was originally a moral theory and evolved from the doctrines of the Confuciuan school (or Zi-Si-Mencius school). Later, In the third century BCE Zou Yan combined and systematized two current theories during the Warring States period: Yin-Yang and the Wuxing.

*personal note: the Wuxing seem to be related to the Eight Trigrams (bagua) from the I Ching, the original version of the I Ching (it was edited by King Wen in 2852 BC) goes back to the supposed writer Fuxi, the legendary ruler.  

A closer look at the Five Phases
Ultimately the natural cycles and interrelationships in both our environment and within ourselves have let to the theory of the Wu Xing. The foundation of the theory rests in the correspondences of each element to a variety of phenomena. 

These “Five Phases” are
Wood (木 mù)
Fire (火 huǒ)
Earth (土 tǔ)
Metal (金 jīn)
Water (水 shuǐ) 

Wood
Wood is flexible, like bamboo. It grows and expands. It is also associated with qualities of generosity and idealism and leadership. It is the leader within us, that can take charge and determine a plan of action. Spring is the season of wood and it is the period of sprouting. The color associated with wood is green. In Chinese Medicine the liver is the organ of wood. 

Fire
In Chinese thought Fire is passionate, it is joy, laughter and playfulness. But also the qualities of dynamism, strength and persistence; however, it is also connected to restlessness. Summer is the season of fire and it is the period of blooming. The color associated with fire is red. In Chinese Medicine the heart is the organ of fire. 

Earth
Earth is patient, thoughtful, practical and hard working. It brings harmony and stability. Late summer is associated with earth and it is the period of Ripening. The Color of Earth is yellow. In Chinese Medicine the spleen is the organ of earth. 

Metal
Metal is unyielding, rigid and persistence.

Metal type people like minimalism. They are organized, clean, and contained. The Fall is associated with metal and it is the period of withering. The Color is white. In Chinese Medicine the Lungs are the organ of metal. 

Water
In Chinese Taoist thought, water is representative of intelligence and wisdom, flexibility, softness and pliancy. Water can be weak like fluid but it can also turn into a flood and overwhelm the land. The winter is the season of water and it is the period of dormancy. The color of Water is black. In Chinese Medicine the Kidneys are the organ of water.  

Elements or Phases
You will often see Wu xing translated as “Five Elements” but the Xíng are primarily concerned with process and change, they are not the same as the   classical Greek elements that are concerned with substances or natural qualities.

The Changing qualities or Cycles are:

Generating  
The Xing are Inter-promoting, often called like mother and child. Wood for example is the mother of Fire. You can easily see this because Fire comes after Wood (clockwise) so in that way Wood feeds Fire, like a mother would.
In this way all the Phases can be listed as:

Wood feeds Fire
Fire creates Earth (ash)
Earth bears Metal
Metal enriches Water
Water nourishes Wood

This Cycle of is called the 五行相生 Sheng Cycle (Generating Sequence)

Controling
Each Phase controls or keeps another element in balance, much like Yin and Yang keep each other in balance. In the Wuxing, it will come as little surprise that Water controls Fire and Metal controls Wood. While some of the others are a bit less obvious, it will become clearer when you understand that the five elements all have specific qualities that go beyond just metal chopping wood.
 
All the elements Controlling sequence can be listed as:

Wood controls Earth
Fire controls Metal
Earth controls Water
Metal controls Wood
Water controls Fire

This Cycle is called the 五行相剋 Controlling Sequence or Father-Child relationship.    

Other than these two cycles, the Overacting Cycle (when an element controls too much) and the Insulting sequence (when for example fire starts heating water instead of water extinguishing fire) also exist.