A chord diagram shows you exactly where to place your left hand fingers in order to play a particular chord. The black dots show you where to place your left hand fingers.The white number tells you which finger to place on the string just before the fret. If there is no dot on a string, you play it as an open (not fretted) string.
A dotted string indicates that string is not to be strummed. An X on the string indicates taht string is to dampened by another finger lightly touching rt The string is still strummed as a part of the chord but it is not heard. A small bar connecting several black dots indicates they are held down by the same finger. This is called barring.