下去 (xià qù) has two distinct uses. Literally it means to go downward (走下去, go down, e.g. stairs). As a directional complement attached to verbs it indicates continuation of an action: 说下去 (continue speaking), 坚持下去 (keep persisting), 活下去 (continue living). This continuation meaning is extremely common in everyday Mandarin. Its complement pair is 下来 (xià lái), which indicates coming down towards the speaker.