The darshanas are the philosophy schools. As against the philosophies that do not account the vedas like lokayata, charvaka etc., these six accept the vedas. They are not necessarily contradicting, but often extending from the one another.
nyAya of gautama – Based on logic to explain the world and God.
vaisheShika of kaNAda – Allied to nyAya and explains how the world is created.
sAnkya of kapila – Lists down 25 tattvas (hence called so). Taken basis by the later mentioned philosophies.
yoga of pata~nchali – Prescribes the yogic practices required to attain the final state.
pUrva mImAsa of jaimini – It is kriya mArgar (path of action) based on the samhita, brahmana and Aranyakas of vedas.
uttara mImAmsa of bAdarAyaNa – It is the philosophy school taking basis upaniShad also called as vedanta.