Vedanta had, by the time of Chaitanya's teaching in early sixteenth century Bengal, produced two major and apparently opposed readings of the relationship between Brahman and the world. Shankara's Advaita held the individual soul and the world to be, at the level of ultimate truth, not different from Brahman at all, difference being an effect of ignorance. Madhva's Dvaita held soul, world and God to be eternally and irreducibly distinct.
Chaitanya, working within the devotional Krishna theology of Bengal, did not choose between these positions. He taught instead that souls and the world are Krishna's own energies, shakti, and that an energy is neither wholly identical with its source nor wholly separate from it, the way heat is inseparable from fire yet remains distinguishable from it.
Jiva Goswami, the most systematic of the six Goswamis whom Chaitanya sent to Vrindavan to give his teaching a formal theological grounding, developed the position at length in his Sat-sandarbha, arguing that scripture supports both identity and difference at once and that the relationship between Krishna and his energies is acintya, inconceivable, not because reason has failed but because the relationship belongs to a kind that ordinary conceptual categories were never built to capture. The term did real philosophical work: it let Gaudiya theology affirm both a personal, relatable Krishna who receives devotion as a distinct beloved, and a Krishna who is, in another and equally true sense, everything that exists.