[Son of Númenor]

Here is a quote that nicely sums up the business & nature of the Istari in Middle-earth:

"...they came from over the Sea out of the Uttermost West; though this was for long known only to Círdan, Guardian of the Third Ring, master of the Grey Havens, who saw their landings upon the western shores. Emissaries they were from the Lords of the West, the Valar, who still took counsel for the governance of Middle-earth, and when the shadow of Sauron began first to stir again took this means of resisting him. For with the consent of Eru they sent members of their own high order, but clad in bodies as of Men, real and not feigned, but subject to the fears and pains and weariness of earth, able to hunger and thirst and be slain; though because of their noble spirits they did not die, and aged only by the cares and labours of many long years. And this the Valar did, desiring to amend the errors of old, especially that they had attempted to guard and seclude the Eldar by their own might and glory fully revealed; whereas now their emissaries were forbidden to reveal themselves in forms of majesty, or to seek to rule the wills of Men or Elves by open display of power, but coming in shapes weak and humble were bidden to advise and persuade Men and Elves to do good, and to seek to unite in love and understanding all those whom Sauron, should he come again, would endeavour to dominate or corrupt." (Unfinished Tales, "The Istari")

My recommendation would be to buy or check out the Unfinished Tales & read this essay in its entirety, & also perhaps to do the same with the Silmarillion, particularly the section "Of the Rings of Power and the Third Age".

Gandalf saying that he is a steward implies that he is a 'caretaker' of Middle-earth, an upholder of morality & goodness, & a leader of the free peoples of Middle-earth in the battle against the forces of evil.