The theory that you've just read about is significantly different from the Stockholder Theory that we saw from Friedman. Let's take a look at Freeman's thesis, and see just how different they are.
"The basic idea is that businesses, and the executives who manage them, actually do and should create value for customers, suppliers, employees, communities, and financiers (or shareholders)." 
I'm sure that you remember Friedman's thesis, but here it is as a reminder.
"There is one and only one social responsibility of business – to use its resources and engage in activities designed to increase its profits so long as it stays within the rules of the game, which is to say, engages in open and free competition without deception or fraud." 
Value v. Profit
You'll notice right off that Freeman's Stakeholder Theory replaces the term profit with the term value. Profit is a measurement in dollars, while value might be measured in all sorts of ways. Think of the sorts of things that you value. I'm sure money is on that list, but it's not the first or the only thing on the list. Probably the top few look like this:
Okay, those last two are probably peculiar to philosophers, but I've asked this question for years to hundreds of students, and "family" is always at the top of the list. Money never has been.
It's obviously true that we value money (and therefore profit), but it certainly isn't the only thing that we value and we don't value it the most. There are other things which are more important to us. If we are to create value for the various groups that Freeman mentions, then that value may be of many different sorts. Some groups will have value created in terms of profits. For some of them it will be appropriate to create value in terms of living conditions, working conditions, pollution, noise, or fairness. Freeman's Stakeholder theory allows us to give consideration to those things that are appropriate to the circumstances. In other words, it will allow us to create positive, lasting relationships with the community that we interact with.
Speaking of relationships, the next thing you'll notice in Freeman's thesis is that he lists several groups of people that corporate executives should create value for: stakeholders. This is a far-cry from the one group that Friedman lists: stockholders. One of the problems with Friedman's view is that he so narrowly restricts the range of relevant groups that it no longer resembles actual business interactions.
A business, even a very successful one, cannot exist in a vacuum. It requires that there be investors to give them money, customers to buy their goods/services, employees to serve the customers, suppliers to sell them the goods that they will sell, and a community within which they can thrive. If any of these groups are absent, the business cannot be successful. Of course, the groups might interact in a hostile way. A retailer could demand such low prices from their suppliers that the suppliers cannot make very much profit on their goods without turning to something like overseas production facilities or making products of inferior quality. Some retailers are able to do this (Wal-Mart, for example), but it fosters a relationship in which the suppliers resent their need to work with the retailer, and they would happily back any other retailer instead if they could make a profit that way. This is not a healthy environment, and it works only so long as the retailer can maintain market-dominance. The interests of all involved would be better represented if everyone's preferences could be satisfied.
It might be argued that the Stakeholder Theory is a better representation of the actual web of relationships that exist in any business' interactions. Of course, the Stakeholder Theory certainly involves more responsibilities than the Shareholder theory. The management that uses Stakeholder Theory is responsible for taking into account the needs and wishes of a great many people. Certainly more groups than just the Shareholders.
Friedman gave us several good reasons to think that businesses should only have a responsibility to increase profits for the benefit of shareholders. In the next section we will take a look at some reasons to think that perhaps we have good moral reasons to take up the extra obligations of the Stakeholder Theory.
1. R. Edward Freeman, "Managing for Stakeholders." In Ethical Theory and Business 8th Edition, edited by Tom L. Beauchamp, Norman E. Bowie, and Denis G. Arnold (New Jersey: Pearson, 2009), 56.
2. Friedman, p. 55.