Chord boxes are diagrams that show which strings to stop, and where to stop them, to play any specific chord. They represent the neck of the guitar, with each vertical line representing one string. The line on the furthest left represents the sixth string, the one next to it the fifth, and so on. Unless indicated otherwise, the line at the top of the diagram represents the nut.
Interpreting chord boxes is pretty simple: each line represents a fret. Dots are drawn where the fingers are supposed to rest. If a string is to be played without stopping it, it is marked with the symbol O. If, however, the symbol X appears next to the string, it is understood that it should be muted or avoided.
Sometimes, each dot will be labeled with a number, representing the finger which should be used. For these purposes, left hand fingers are referred to as 1, 2, 3, and 4 (index, middle, ring, and little, respectively).