means,

Consisting of spirit; not material...
(as a spiritual substance of being. The soul of man is spiritual.)
Mental; intellectual... (as spiritual armor. Eph 6)
Not fleshly; not material...
(as spiritual sacifices. 1 Pet 2)
Pertaining to the renewed nature of man... (as spiritual life)
Pertaining to divine things... (as spiritual songs. Eph 5)

(See more in Wenster's 1828)

Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God. Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual.
1 Corinthians 2:12-13