What is it?
Tapping is a hammer-on with a right hand finger, 1st or 2nd. It is notated as a slurs with the symbol "T".
For more detailed information you can read this page on Wikipedia.
How to play it
Tap down on the fretted string with the index or middle finger of the right hand. This is usually followed by a pull-off to sound a lower note.
Below is the first example of tapping on the E string. Tap the first note to the 12th fret then pull the string to play the 5th fret pressed by index.
And below move the right hand to tap the indicated frets. Tap 4 time every fret.
Pay attention to mute the 2nd open strings by putting the finger on them.
Tap now these frets.
Play now this solo on the first string.
And below move the fretted hand.
Be careful to synchronize well the movements and play very slow.
Now you have to play three notes.
Tap the 12th fret, pull to open string and then hammer the frets with the right hand.
Here is a good and nice exercise to train your fretted hand
The exercise below shows a movement widely used in tapping.
Tap, pull, hammer, without open strings. Play very slow first.
Here below a nice guitar solo all played with tapping.
If you learn to play well this, then you're ready to play harder solos.