When I talk about the levels of play, I mean that there is a simple level of the Dungeon Crawl - stay at the inn, catch rumors at the tavern, go to store, outfit your party, go to the Dungeon, kill the monster, get the treasure, buy more stuff, back to the Dungeon. So goes the Dungeon cycle. As the players advance in level, they can Hex Crawl and go to other places in the fantasy world, and find other taverns, chase more rumors, and find another dungeon whilst exploring hexes. The DM's world expanded as the players advanced in level. The level of the Sandbox occurs in the story space between the adventures, and the gaming that takes place involves the players interacting with the setting, while spending gold and skill points to develop their characters. Let's say that your 5th Level Fighter wants to step up to the next level of his weapon specialization. Through role play, the player realizes that he has surpassed his current fencing instructor, but the Master tells the player of HIS teacher, and now the players must journey a long way on a quest for the Fighter to find his new teacher. This kind of gaming was not provided for in the vanilla editions of D&D, everyone sort of levels up automatically and acquires new abilities. This is the Sandbox, it helps the D&D cvampaign side-step what Dave Arneson criticized about D&D - get treasure buy bigger sword to get even more treaisre to buy even a greater sword.
The biggest fallacy of the OSR is that there is no story in traditional D&D - Dungeon Crawls and Hex Crawls. After all, a DM draws a map of the labyrinth, keys the areas in it, makes notes as to what Monsters, Traps, and Treasures the labyrinth contains. DM then creates a small towm to serve as the base for the players cum adventurers. Simple world, then as the players advance in levels, the DM craws the map of the adjoining areas and the players engage in hex crawls or wilderness exploration. This creates an illusion that there is no story in an old school D&D game, but it is wrong. This is a form of story-telling - where the rooms provide critical incidents and the corridors connect the incidents with each other. It might be a non-linear, non traditional story, but it is still a story. It becomes even more of a story, when a DM desides to flesh out a theme or a back-story for a dungeon, when DM creates an adventure for the players that gives them a reason to enter thr labyrinth, and defeat what is there. DM doesn't even think of how he or she is telling the story within the parameters of the Dungeon Adventure. The unique format of the Dungeon Crawl and the way it formalizes and processes the DM-player storytelling interaction is the reasom behind the remarkable success of the Dungeon design/Dungeon Adveture format. The further we move away towards representing more complex adventures and situations, the harder it becomes and the weaker the game mechnics of adventure design become. Gygax and Moldway did not write anything as good for Wilderness design as they did for the Dungeon Adventure, and the Second Edition folks and beyond did even less for the non-linear non-tactical adventure design, ot the node-based adventure design, that represntes the schematics of an Event-based as opposed to the site based adventure design.
Brooser's Sandbox partly consists of fleshing out the setting in which event based adventures and character development can take place, and then forcing the players to traverse the wilderness between points where critical encounters in the adventure take place in accordance with the traditional rules for D&D travel.