Sanchin is the classic stance of Goju Ryu. It is used in all the Kata and is the starting point of most Kata, often used as the first three moves.Many students are often confused by Sanchin and wonder what the fighting applications are. This is perhaps the wrong way to look at the Kata. Sanchin was probably a Chi Gung (energy exercise) Kata originally. It's purpose to develop breathing, balance and posture (hence three battles).
Within this trinity would be a great many lessons and Sanchin should be considered a training Kata/stance. Within Sanchin are the elements for all other Karate technique hence its importance. It is the engine that drives the technique and should be thought of as a 'turn key' or a fundamental form.
Breathing; 'all is breath', as the Chinese say. Good breathing develops stamina and strength and oxygenates the body for pre-longed combat. The Chinese also believed you could breath in Chi energy and circulate it around the meridians of the body. This breathing and Chi energy would be used in the old days for 'Iron Shirt Training' the ability to withstand blows. Today we have a different view of how the diaphram helps breathing, but the principles are still the same.
Balance - this is more than just the obvious facility of stability and probably refers to the balance of Chi around the body. It is probably also a metaphors for balance within your training and life. Balance of the muscle groups for correct power delivery. Balance of the mind in assessing situations. Balance of contraction and relaxation or 'Isometrics' as we call it today.
Posture - again it was believed that without good posture Chi cannot flow. This makes sense, in that without proper alignment, the body cannot operate at maximum efficiency. Sanchin is full of 'Critical Angle' postures that affect the strength/power (Chi) of all moves.
Think of Sanchin as a spiritual, physical and emotional training Kata and it will take you a life time to master and enjoy.