Arpeggios in Guitar

Arpeggios is a great form in music.
The word arpeggio (ar-peh-jee-oh) comes from the Italian word 'arpeggiare' which means 'to play harp'
You will learn arpeggios in intermediate stages on your learning process. Its a great way to add color to your playing, basically arpeggios is a broken form of chords simply notes of the chords played individually not strummed together.
In arpeggios you have to play only the chord notes on a particular chord,

Example - In G major chord you have to play the arpeggios form only using the notes G B D 

In Cm chord you have to play the arpeggios form only using the notes C D# G like this.

In guitar major triad and minor triad are most common chords for playing arpeggios. When you are beginner in playing arpeggios always start with the root note and end on the root note that means start on the low pitched root note, play up according to the time signature then go back down then back up to the root note.

Arpeggios can be played in ascending, descending order or randomly.
Arpeggios can be played in different time signature and in different speed, arpeggios can play in slow style and also fast style and for more improvisation arpeggios are played with the passing note its sounds very beautiful and its add more color on your playing. Passing note means suppose your playing C major chord, in that progression you have F major chord on the next bar then what you can do.. You can play C D E note individually before hold the F major chord but remember one thing you have to do this on time whatever the time signature is you have to maintain the rhythm.
You can play arpeggios in different ways like alternate picking, sweep picking ,  tapping, finger picking , pull off, legato.

At first start play slowly gradually you can add speed on the fast arpeggios pattern, practice hard and daily for best results and practice until you are totally confident and controlled on the playing.