According to Shaiva Siddhantam, "Shiva" is the ultimate reality or the singularity from which everything emerges and to which everything returns. This emerging energy is called the "Shakti" (Shiva's consort). Shiva brings forth Shakti, which is essential for the manifestation of all things in the universe. Therefore, it is said that Shiva created Shakti, and in turn, Shakti created Shiva. The fusion of the words "Shiva" and "Shakti" into ShivShakti can provide a comprehensive understanding of this.
Shakti is the energy of Shiva from which all other gods and goddesses, including Vishnu and Brahma, emerge. Therefore, Shiva is considered the father and symbol of masculinity, while Parvati (Shakti) is the mother and symbol of femininity. Shiva is formless, infinite, and represents the unchanging absolute Brahman, while Shakti is the energy of Shiva that creates, protects, destructs, conceals (through maya), and blesses everything. Shiva and Shakti are both the same and different, representing duality.
For example: on a typical day, your body performs a multitude of functions, such as breathing, blood circulation, digestion of food, and sleep, among others. However, you may not be aware of all these processes all the time since they happen naturally. This life energy is generated by you (your soul) so that you can live. If these functions are not working properly or cease to function altogether, then the human body can no longer be called a person, but rather just a "body." The soul is represented by Shiva, and the life energy in your body is represented by Shakti. When the energy stops working, the soul will depart, or when the soul decides to leave, the energy will stop working. Without the presence of energy, we cannot recognise a soul, and without the presence of a soul, we cannot observe the workings of energy. This is why it is said that everyone has Shiva and Shakti within them, because what we perceive outside is merely the body, controlled by the ShivShakti from within.
This concept is depicted in a simpler form through Ardhanareeshwara in Indian temples, particularly those found in South India. This deity appears as a single entity, with Shiva covering the right half and Shakti covering the left half. This duality concept is not limited to religion, as it can be applied to almost everything in the universe. I've written about this in detail here.
To gain a better understanding, consider standing in front of a tasty and aromatic food that looks great. In this scenario, the food represents Shiva, while everything you enjoy about the food represents Shakti. Now, imagine removing the Shakti from the food and what you'll be left with. Without its aroma, taste, and exciting appearance, that would be no longer called food.
Lord Natraja is the embodiment of Shiva's cosmic dance, wherein Shiva dances endlessly through his Shakti to fulfill his five cosmic duties of creation, preservation, destruction, concealment, and salvation. In the depiction, His right leg is firmly on the ground while His left leg is lifted in the air to dance. The right leg represents Shiva, which is still, while the left leg represents Shakti, which is dancing and performing the five duties (Panch Kriya). Only one ancient temple in India, located in Chidambaram, Tamil Nadu, is dedicated to Lord Shiva in his Natraja form. The ancient's call this temple the secret of cosmos (Chidambara Rahasyam) due to the reason we discussed above.
Lord Natraja represents the underlying philosophy of Shaivism. There are 36 tattvas used in Shaiva Siddhantam for a profound understanding of this philosophy. According to the Siddhanta, one can surpass the cycle of time, death, and rebirth by transcending these 36 tattvas.
In Vedic culture, the union of a man and a woman in marriage is seen as the union of Shiva and Shakti.
The soul represents Shiva, the life energy represents Shakti, and our physical body acts as the platform for them to perform actions, represented by Lord Ganesha. This is what is called "AUM", the Pranav Mantra. A represents Shiva, M represents Shakti and U represents Ganesha, the third entity that holds Shiva and Shakti in a perpetual unity.