These chords are called "Open Chords" because they have some open strings (unfretted strings) that ring open.
These are the most common chords on the guitar, and usually the first chords anybody learns.
The "X" in the diagram means that the string is not played. You have to either mute the string with one of the fingers on your left hand, or simply do not strum it with your right hand.
Open chords can only be played in the open position (At the nut of the guitar). However, you can use a capo to transpose (move over) the pitch of the whole guitar upward to any tone, and play the open chords in any key that way.
The fingers of the left hand are numbered as follows. The number inside each fretted note (Dot on the diagram) is the finger you use to fret that note.