What is shakti? Root verb is 'shak': to be capable, so shakti is power or capability. The fundamental shakti that enables Manifestation of Brahman is AvaraNa shakti and vikshepa shakti. AvaraNa comes from vR (to cover), so it is the power to conceal the true nature of Brahman as Consciousness. Vikshepa shakti comes from kship (to throw) and vikshepa is projection. From the play of Rajas guNa, Brahman has the power to project the external world. These two shakti's are attributed to mAyA.
Once manifested, we encounter other forms of shakti. Shakti can be experienced at the level of each of the koshas: so we have great physical strength or bala in the annamayakosha, great energy or vitality in the prANamayakosha, and great mental strength of will in the manomayakosha.
The conceptualization of Manifestation as a play of Shakti and Shiva is found in the Tantra or Shakta tradition. This is also called LIla (play).