It its known that the Istari were sent to Middle Earth to aid in the battle against Sauron, being only allowed to inspire and no direct actions could be taken.
But, why is this? Could this rule be broken? Did Eru himself create the rule?
The problem that the immortals had discovered, from their previous interventions, was that they didn't work. They tended to wreak havoc across the land, but only served to change the current power structure, not remove it. By intervening directly, they could not change the nature of people, and there was a danger that they would be relied on to always save the world in time of need.
The Istari were another approach, of trying to provide guidance and influence, so that the residents of Middle Earth could do their own work, and could be slowly but gently guided towards the right way, without any direct intervention. This means that they would win the victories primarily on their own, and would not rely on or expect help from over the sea.
In many respect it worked. The last battle was a combination of many forces, all of whom needed to separately see their need to fight, but who could all fight for one cause and one purpose, which was Middle Earth itself.
The "rule" was more of a charge, an ideal that they were supposed to hold to. The reason behind this is stated in the Wikipedia:
They had tried direct intervention in the destiny of the Elves in the Years of the Trees by leading the Eldar into the West, but this resulted in many bloody wars and confrontations. In the struggle against the Dark Lord, they hoped instead to help Men achieve their own destiny. Thus Gandalf and the other wizards were meant to use their great wisdom to persuade Men to courses of action which would achieve Men's own goals, rather than trying to dominate them.
As far as the rule being able to be broken, that is exactly what Saruman did:
Saruman failed in this when he tried to set himself up as a commander in opposition to Sauron, but Gandalf remained faithful to his charge.
I know that in the beginning of the Silmarillion, Eru created the Ainur and subsequently through the Music of the Ainur, layed a plan for the world that was to be created. In my interpretation (and i'm sure others as well) it was Melkor diverting from the song and doing his own individual will that was the starting point for all the strife in the world that came afterwards.
I would argue that the Valar and maybe Eru himself, try to "stick to the plan" as much as possible. In this specific example, I would say that because the war against Sauron was not in the original music/plan the Valar try to keep their distance and manipulate the situation instead of directly getting involved and diverting even further from the original song.
The canon knowledge of the restrictions upon the Istari largely come from the relevant passages in Unfinished Tales. Manwe asked
Who would go? For they must be mighty, peers of Sauron, but must forgo might, and clothe themselves in flesh so as to treat on equality and win the trust of Elves and Men. But this would imperil them, dimming their wisdom and knowledge, and confusing them with fears, cares, and weariness coming from the flesh.
From that it is obvious that they shall have restrictions, and they were imposed by Manwe or higher, i.e. potentially Eru.
This rule could definitely be broken - Saruman did not forgo might, nor treat on equality with Elves and Men. And given such, he failed the task set upon him and the other Istari.
As to why the rule was set, we can only speculate. The reasoning for this is not explicit in Tolkien's writings, so we cannot know whether it was:
In my opinion it was most likely the latter given what we saw of Saruman and the mention of the Blue Wizards being the cause of dark magic sects, but it is purely speculation.