Draws a border around the equation and fills it in, so the equation sits on its own background rather than over whatever is beneath it.
An equation is drawn on a transparent background, so gridlines, shading and anything else on the sheet show through it. Box gives it a background and a thin black border.
By default the background is taken from the cell the equation belongs to, not simply white. Put an equation over a shaded block and the box matches the shading; over a plain sheet it is white. This is what stops a boxed equation on a coloured table from appearing as a white rectangle cut out of it.
That default, and two other things about the box, can be changed in Settings — see The box settings below.
A locked equation is outlined whether it is boxed or not, so you can see at a glance which equations will not be redrawn. Its border is dashed rather than solid.
Three settings under Box in the Settings panel. All three apply wherever a box is drawn — to equations rendered on the Formula tab and to equations written on the LaTeX tab alike.
Box does two things at once. It becomes the setting every equation you render from then on is drawn with, and it is applied immediately to the equations belonging to the cells you have selected.
So to change existing equations, select them — or a range covering them — and then tick or clear the box. To change only the default, tick it with an empty cell selected: there is nothing there to reformat.
If a boxed equation has the wrong background, the cell's fill has changed since it was drawn. Select it and tick the box again, or redraw it.