We can answer this question only by turning to the Holy Scriptures, which, being inspired by the Paraclete, gradually reveal his action and identity to us...
...The most original feature of biblical revelation is to have recognized history as the privileged realm for the action of God's Spirit. In about 100 passages of the Old Testament, the ruach YHWH indicates the action of the Lord's Spirit guiding his people, especially at important turning points in their journey.
Thus in the period of the judges, God sent his Spirit upon frail men and changed them into charismatic leaders invested with divine energy; this is what happened to Gideon, to Jephthah and in particular to Samson (cf. Jgs 6:34; 11:29; 13:25; 14:6, 19).
With the arrival of the Davidic monarchy this divine force, which until then had been manifested unpredictably and sporadically, acquired a certain stability. This can be clearly seen in the royal consecration of David, of which Scripture says: "The Spirit of the Lord came mightily upon David from that day forward" (1 Sm 16:13).
During and after the Babylonian exile, Israel's whole history is reread as a long dialogue between God and the people chosen "by his Spirit through the former prophets" (Zec 7:12). The prophet Ezekiel explains the link between the Spirit and prophecy when he says, for example: "And the Spirit of the Lord fell upon me, and he said to me, 'Say, Thus says the Lord...'" (Ez 11:5). But the prophetic vision looks above all to that privileged time in the future when the promises will be fulfilled under the sign of the divine ruach.
Isaiah foretells the birth of a descendant on whom "the Spirit of the Lord shall rest ... the spirit of wisdom and understanding, the spirit of counsel and might, the spirit of knowledge and the fear of the Lord" (Is 11:2-3)... The Messiah of the lineage of David ('from the stump of Jesse') is precisely that person on whom the Spirit 'shall rest'" (Dominum et Vivificantem, n. 15).
Two marks of the mysterious identity of the Holy Spirit can already be seen in the Old Testament and are then amply confirmed by the revelation of the New Testament.
The first mark is the absolute transcendence of the Spirit, who is therefore called "holy" (Is 63:10, 11; Ps 51:13). The Spirit of God is in every respect "divine". He is not a reality which man can acquire with his strength, but a gift which comes from on high: he can only be invoked and received. Infinitely "other" with regard to man, the Spirit is communicated with total gratuitousness to those who are called to co-operate with him in the history of salvation. And when this divine energy finds humble and ready acceptance, man is stripped of his selfishness and freed from his fears; truth and love, freedom and peace flourish in the world.
Another mark of God's Spirit is the dynamic power he reveals when intervening in history. At times there is a risk of projecting onto the biblical image of the Spirit concepts tied to other cultures, for example, the concept of "spirit" as something evanescent, static and inert. The biblical concept of ruach, however, indicates a supremely active, powerful and irresistible energy: the Spirit of the Lord, we read in Isaiah, "is like an overflowing stream" (Is 30:28).
Therefore, when the Father intervenes with his Spirit, chaos is transformed into cosmos, the world comes alive and history is set in motion.