Shakti or Adi Shakti is the primordial cosmic energy and represents the dynamic forces that are thought to move through the entire universe in Hinduism. Shakti is the concept, or personification, of divine feminine creative power, sometimes referred to as 'The Great Divine Mother' in Hinduism. On the earthly plane, Shakti most actively manifests through female embodiment and creativity/fertility.
She is originally mother of trimurti as per Devi Bhagwat Mahapurana but her complete manifested human form also known as sagun swaroop of Adi shakti i.e. Durga is the soul mate of Lord Shiva.She is nature and hence is also known as Prakriti.
Adi Shakti appears in the form of the human form she has taken for Lord Shiva.
She is actually formless.She is also depicted as a lady in red saree with many ornaments and has 8 hands, 7 hands holding different weapons and the lower right hand giving blessings.
When the world was being created, Lord Bramha asked Lord Shiva for a boon. Lord Bramha asked Lord Shiva to separate Shakti from him(Shiva) as Bramha needed energy(Shakti) to create the world.Thus,Shakti was separated from Shiva.
After the world was created, it was decided that Adi Shakti should again be united with Shiva. Therefore, Adi Shakti took the incarnation of Sati,in order to win Shiva over. But,unfortunately and tragically,Sati died,which made Lord Shiva so sad that he decided to renounce the world and began meditating.
To get Shiva out of his meditation and to engage him with the world,Adi Shakti again took the human form of Parvati.