This Greek name of God can be translated in two ways. God is the Father of spirits in the sense that He created each one of us. He is also our Spiritual Father. God is spirit and we are to related to Him as our Father in spirit and in truth.
Father of spirits in Greek:
Ho patēr tōn pneumatōn
Strong’s Concordance numbers: 3962, 4151
Bible reference: Heb. 12:9
We have had fathers of our flesh which corrected us, and we gave them reverence: shall we not much rather be in subjection unto the Father of spirits, and live? (Hebrews 12:9 KJV)
Some other versions translate this name of God as Our Spiritual Father (NEB/JB).
Similar names of God in the Old Testament are the God of the spirits of all flesh and God of all flesh.