There are two main types of chords, open chords and bar chords. Open chords are named this because they have at least one string in the chord which is played open (no fingers pressed on any fret). Have a look at the "Basic Chords" section and you will see all chords written there have a least one string which is not pressed down (played open).
When you play a bar chord you are pressing all the string down in the chord you're playing, not one is left open. Because of this you can move the chord shape up and down the neck of the guitar, this is also called a movable shape.
There are five main bar chord shapes you can play, E Shape, A Shape, C Shape, D Shape and G Shape. All these shapes are your five main open major chords. For now we'll only focus on the first three.
E Shaped Bar Chords
The 1st finger is acting like the nut, holding down all six strings. Because all six strings are being held down you can now play this chord on any fret you choose.
Let's break this bar chord up into two sections, the bar which is made by the first finger laying across the six strings, and the extension which is made by the second, third and fourth fingers. In this case you can see the first finger is going across all six strings, so it is taking over the roll of the nut. The "E" shape is moved up one fret, we will call this an "E" shape the extension. You should be able to see why this chord is given the name of an "E shaped bar chord". To think of it another way you are just shortening the length of the strings by one fret, and what is one fret higher than "E"? .............. "F". It is also the same as placing a capo on the 1st fret and then playing you "E" chord.
The same idea applies with the "A” shape bar chord, but the 1st finger only need to go across five strings. It can also go across the sixth string but make sure you only sound out the five. When I play this chord I place the tip of my 1st finger on the 6th string. This mutes the 6th string and I am able to include it when I strum because it doesn't sound out now. This way I don't have to focus on the right amount of strings to strum.
The "C" shape bar chord is the least used of the bar chords, but I think in some ways it can be more important. Playing this bar chord will later help you to transpose chord progressions easier. It will help link up relative Minors and Majors, (which is useful for soloing) and most importantly it is a nice sounding bar chord.