Tehillim 51:12 "Create a pure heart for me, O G-d, and a steadfast spirit renew within me. 13 Cast me not away from Your Presence, and take not Your holy spirit from me."
The Ruach Hakodesh is divine inspiration or prophetic inspiration and is not the same as what is taught in Christianity as in the doctrine of the Trinity. No where in the Hebrew Scriptures is there any reference to a spirit divine in itself or 'Holy Ghost', as distinct from a spirit that comes from G-d to inspire human beings.
For example, in Shemot 35:31, where it refers to Betzalel, the architect of the Mishkan, being filled with ruach Elokim...the meaning is that he was filled with a spirit which came from G-d to guide him in his task. This is the meaning in Rabbinic literature, where the term denotes a level of divine inspiration.
The books of Tehillim and Mishlei were compiled under the Ruach Hakodesh, i.e., by a degree of inspiration, somewhat less than the degree of prophecy, although on occasion, the prophetic vision itself is also said to be by means of the Ruach Hakodesh.
Maimonides (Rambam, Guide of the Perplexed, 2. 45) lists the Ruach Hakodesh as a degree of prophecy but understands it in a more or less rationalistic manner as a certain thing that descends upon an individual, 'so that he talks in wise sayings, in words of praise, in useful admonitory dicta, or concerning governmental or divine matters - and all this while he is awake and his senses function as usual'.
With the passing of the last three prophets (Chaggai, Zechariah, Malachi) the Ruach Hakodesh is said to have departed from Yisrael (Tosefta, Sotah 13:2; Sanhedrin 11a) and subsequent revelations were given by a Bat Kol, a mysterious heavenly voice.