The benevolent dictator model is exactly what it sounds like: final decision-making authority rests with one person, who, by virtue of personality and experience, is expected to use it wisely.
Although "benevolent dictator" (or BD) is the standard term for this role, it would be better to think of it as "community-approved arbitrator" or "judge". Generally, benevolent dictators do not actually make all the decisions, or even most of the decisions. It's unlikely that one person could have enough expertise to make consistently good decisions across all areas of the project, and anyway, quality developers won't stay around unless they have some influence on the project's direction. Therefore, benevolent dictators commonly do not dictate much. Instead, they let things work themselves out through discussion and experimentation whenever possible. They participate in those discussions themselves, but as regular developers, often deferring to an area maintainer who has more expertise. Only when it is clear that no consensus can be reached, and that most of the group wants someone to guide the decision so that development can move on, does she put her foot down and say "This is the way it's going to be." Reluctance to make decisions by fiat is a trait shared by almost all successful benevolent dictators; it is one of the reasons they manage to keep the role.
Being a BD requires a combination of traits. It needs, first of all, a well-honed sensitivity to one's own influence in the project, which in turn brings self-restraint. In the early stages of a discussion, one should not express opinions and conclusions with so much certainty that others feel like it's pointless to dissent. People must be free to air ideas, even stupid ideas. It is inevitable that the BD will post a stupid idea from time to time too, of course, and therefore the role also requires an ability to recognize and acknowledge when one has made a bad decision — though this is simply a trait that any good developer should have, especially if she stays with the project a long time. But the difference is that the BD can afford to slip from time to time without worrying about long-term damage to her credibility. Developers with less seniority may not feel so secure, so the BD should phrase critiques or contrary decisions with some sensitivity for how much weight her words carry, both technically and psychologically.
The BD does not need to have the sharpest technical skills of anyone in the project. She must be skilled enough to work on the code herself, and to understand and comment on any change under consideration, but that's all. The BD position is neither acquired nor held by virtue of intimidating coding skills. What is important is experience and overall design sense — not necessarily the ability to produce good design on demand, but the ability to recognize and endorse good design, whatever its source.
It is common for the benevolent dictator to be a founder of the project, but this is more a correlation than a cause. The sorts of qualities that make one able to successfully start a project — technical competence, ability to persuade other people to join, and so on — are exactly the qualities any BD would need. And of course, founders start out with a sort of automatic seniority, which can often be enough to make benevolent dictatorship by the founder appear the path of least resistance for all concerned.
Remember that the potential to fork goes both ways. A BD can fork a project just as easily as anyone else, and some have occasionally done so, when they felt that the direction they wanted to take the project was different from where the majority of other developers wanted to go. Because of forkability, it does not matter whether the benevolent dictator has control over the currently accepted "master" project repository. People sometimes talk of repository control as though it were the ultimate source of power in a project, but in fact it is irrelevant. The ability to add or remove people's commit passwords for one project on a particular hosting site affects only that copy of the project on that site. Prolonged abuse of that power, whether by the BD or someone else, would simply lead to development moving to a different copy of the project.
Whether your project should have a benevolent dictator, or would run better with some less centralized form of governance, largely depends on who is available to fill the role. As a general rule, if it's simply obvious to everyone who should be the BD, then that's the way to go. But if no candidate for BD is immediately obvious, then the project should probably use a decentralized decision-making process, as described in the next section.