The Hotbox provides quick access to some settings that, frankly, we couldn't figure out where else to put. To show the hotbox, hold down the spacebar and it will instantly appear. Release the spacebar and it will disappear. Simple! An annotated image is shown below.
You can also press and release Shift+spacebar to pop up the Hotbox in a semi-persistent mode. In this mode, the hotbox will remain visible until you click in the scene somewhere outside of the box, without the need to hold the spacebar down.
Most of the top row of buttons are Camera Controls, see that page for details. The far-right button is the scene Backround Color. Click on this colored rectangle and a color-picker will open, allowing you to set the background color.
The second row is broken up into two sets of mutually-exclusive buttons. the Normals setting determines which type of surface normals are used in the rendering of meshes. The first option is Smooth Vertex Normals, which work great on smooth surfaces but don't work at all if your mesh has sharp edges, particularly if it has a low-resolution CAD triangulation. The second option is Triangle Normals. In this mode each triangle is shaded separately, which means the facets in your mesh will be clearly visible. This is the default. Finally we have Face Group Normals. In this mode, we use smooth vertex normals on the interior of each facegroup, but at the borders of facegroups, we estimate normals separately for each side. As a result, facegroup borders that lie on creases in the surface will appear as creases in the rendering.
The Color setting determines which color mode is in use. There are two options, the first is Vertex Colors, which show the per-vertex colors that you can either import with your mesh, or interactively paint with the brush tools. The second option is Facegroup Colors. In this mode, each facegroup is rendered in a different color, and the vertex colors are hidden.
Finally, the bottom row has quick-access sliders to the current Brush Size and Strength. These are handy if you are in the middle of sculpting and don't want to have to go all the way back over to the properties panel.