The term – ARDHANARISHVARA is a combination of three words –ARDHA , NARI , ISVARA which means HALF, WOMAN, GOD respectively.
Ardhanarishvara is the god whose half is woman ,indicating that It is male (SHIVA) and female (SAKTHI) who are inseparable;there is no existance in absense one or the other.
The Buddha taught that each human being has a right and left hemisphere in the brain, which we classify as male and female, the right being female, left being male. The left or male side is in charge of the right side of the body and the right brain or female side is in charge of the left side of the body.
The Mayan placed themselves and their environment into categories using the basic complementary pairing of male/female, and right/left.
In yoga male energy (the sun), is referred to as Shiva, and is the form of the universe. Male energy is the domain of the right side of the body. Whereas female energy (the moon), is referred to as Shakti, and is the force of the universe. The female energy is the domain of the left side of the body.
The significant importance is that as one person we need to be in constant balance to be able to achieve the best of our world, mental physical and emotional. Both sides, male and female have to attain a harmonious whole.
That’s why our ancestors even years before the discovery of this gender balance ,depicted a god symbolically to say that no one human has a perfect gender, and empasising to balance best of both.