While the gaming style is old the term Sandbox, applied to RPGs, is very new. Sporadically threads will appear about sandbox campaign on various forums. While some start worthwhile conversations many degenerate into rants with various antagonists intent on slagging each other. A recent thread on theRPGsite is more the former than the latter.
My point of view on Sandbox Campaign is somewhat limited. I view it as a method of organizing your setting in a way that makes it easy for you to referee when players go off wandering on a tangent. It is a compact way of organizing local information about a region.
Most threads on Sandbox campaign talk about the style of the campaign run using this format. Basically the big misconception is that referee is essentially a simulator running the NPCs and monster as the players wander from point to point. There is no plot adventure only happens when players run into a spot where it is located. Most folks write that when they try this the result are a bunch of unhappy players who are bored.
Most of the time this because the referee is too passive and the player don't context in which to decide where to go. Player that are highly motivated can make this work and sometimes this results in a great campaign. However most of time it doesn't work so well.
The Sandbox format can be used to create any type of campaign. You can even make a railroad out of it by having all your locales obviously point to a certain director or event. Some campaign go the realistic route and write up the locales as they were a slice of a living breathing world. Paizo's Kingmaker has many locales have clues about the ultimate menace of the adventure path. Other are a slice of life design to be exploited by the players as they build a kingdom in the Stolen Lands. And there are few randoms stuff thrown in to liven the mix.
I use the Sandbox format to create a setting to immerse the characters in. My style is that character are part of a living world where their choices have consequences both good and bad. If they choose to do nothing then world will simply go about it's business indifferent (and sometimes hostile) to character's well being. But if they choose to be involved then they will make a difference and leave their mark on the setting. I developed this because I found players love when their decisions have meaning.
The Sandbox format I use to describe the Majestic Wilderlands isn't enough. I need to add other techniques to make this work. First I work with each player individually to develop a background of about a page length. This give them the context in which to make their initial decision of where to go and what to do.
Second I generally insist on folks speaking in first person and roleplay, however bad their acting is, the character. More than a few just play a fantasy version of themselves which is OK, the important point they are actively interacting rather then looking at their characters as figures to pushed around.
Third is called "World in motion." I didn't make up the term. Lord Vreeg coined the term in response to a post of mine on theRPGSite. Basically a World in motion has events unfolding and NPCs living their lives outside of what the players are doing. You sprinkle news of what going throughout NPCs conversations or props like billboards or news items. Note that these events can be very local in scope. They don't have to be global.
World in Motion is how a referee injects a plot into his sandbox campaign. Rather being a choice of adventures the "plot" unfolds around the character through the events of the campaign. It is up to the players to interact with these events and resolve them however they like.
Fourth, culture and religion are important in my campaign. The conflict between different values both on a global and local scale provides many seeds for adventures. The background material that goes into this also give character additional stuff to use in interacting with the Majestic Wilderlands.
Your sandbox campaign may mix in other techniques to create your own unique mix. What is important is to remember that is a tool that has certain strengths. I think it is an underdeveloped tool, long ignored until recently. But in the end it is just one of many choices you have to organize a campaign.