Mysterious, inscrutable, arcane mean beyond one's power to discover, understand, or explain.
Something mysterious excites wonder, curiosity, or surmise yet baffles all attempts to explain it.
Something inscrutable defies all one's efforts to examine or investigate it and leaves one with a sense of hopelessness or defeat.
The word is often applied to a person whose intentions, motives, or mental processes are so well concealed that they defy interpretation.
Something arcane is beyond comprehension because known or knowable only to the possessor of the secret (sometimes by implication God, Nature, the Fates, or the authorities). The word may come close to occult in meaning, but it stresses the reservation of what is necessary for comprehension rather than the supranatural or magical character of what is not understood.