The Muslim Brotherhood has been illegal in Egypt for decades.
Since Mubarak began to teeter on the edge of demise, the MB has risen up to lead much of the protesting. It is certainly a large, and potentially quite influential force in Egypt.
Thus far, it has been a relatively moderate force, with relatively moderate discourse.
The West's fear in general is that the MB appears moderate and inoffensive only so that it could stay off Cairo's radar during the past 30 years, and that further down, there is a more strict Islamist agenda.
Whether that's true is tough to say. Other MB organizations have (likely) been indirectly involved with extremist-style violence, and have generally advocated for strong Islamist states.
The Egyptian Muslim Brotherhood started hitting the PR trail virtually as soon as the protests began. They maintained popularity in Egypt despite the ban, and have the potential to be a formidable force in the next round of Egyptian politics.
The risk, of course, was that a power grab (especially early) could make both Western countries and the Egyptian Army sufficiently worried that anti-MB opposition might arise. Given that the Army is far and away the most powerful political group in Egypt, staying on the Army's good side will be critical to avoiding a drag-out political war.
And so, the MB's media office released a statement: "We are not seeking power." They've promised to not field even field a presidential candidate in the next election, and have declared that, "we reject the religious state."
In this move, the Egyptian MB has moved itself far from other Muslim Brotherhood organizations. Ultimately, the Egyptian MB no longer needs as much external help as it once did--it is no longer illegal, and enjoys great popular support in what may become a semi-functional democracy before the year is through.
These moves of reassurance will keep pressure off the MB as it establishes a stronger legitimate presence, and will likely gain even more popularity by being seen as a force that exists to help the common Egyptian citizen.
It's a strong enough stance that it's one the MB would struggle to pull away from (without appearing to betray its its promises). But there is certainly no reason that the MB should not field a presidential candidate in the second presidential election, nor take a significant holding in Parliament in this first election, even if it is unlikely to change its agenda in the short term.