I know what an arpeggio is. What does it mean to practice them? I always hear people talking about it. Do you just practice going up and down the keyboard playing them or what? How do you know which chords to play? I've been confused about it for a while but I always hear how beneficial it is, so I figure I oughta start.

When I first started doing it, I would do one hand at a time, up 3 octaves, down 3 octaves, then do block chords of root, 1st inversion, 2nd inversion, root again (going up). After I got one hand smooth, I did the other hand, then both hands together. I did this for all major and minor keys using standard fingering that my teacher gave me, which I'm sure you could find on-line.

Once I got that fairly smooth, I started working with the metronome, doing 2 octaves up and down in 8th notes, 3 octaves up and down in triplets, and 4 octaves up and down in 16ths. If you've never done it before you need to start out slow, 50 or 60 bpm, then gradually build up speed.

Good luck!

Oooo!! Arpeggios are so cool! Even if you totally stink as a pianist and can't stumble through "Happy Birthday" without starting over, you can wow the folks in the cheap seats with a few arpeggios.
So far I'm only practicing them in the major and minor keys I'm likely to play in (C, G, F, D). If any of my music is in other keys, I just choose another piece!

But, seriously, running up and down the keyboard on these exercises is great practice for smoothness, speed, and musicality. Plus, your ear improves dramatically as you rehearse them.

It is always good to play the chord of the arpeggio you are about to play, e.g.

G
E
C,
then: C E G, C E G, (then down) C G E, C G E C

To learn arpeggios is to also develop fluency in tucking the thumb in when going up the keyboard with the Right Hand and the fingers 3 & 4 over when going down with the same hand (the same concept applies to the LH where fingers 3 and 4 need to go over smoothly ascending and the thumb/finger 1, tucked inside when descending).

Good, subtle wrist movement when putting thumb under/fingers over is also important in Arpeggio playing.

Hope this helps

Arpeggios are a great scale to practice as they feature a lot in pieces in both left hand and right hand sections. Normally as a bass figure in your left hand.

The Associated Board of the Royal School of Music, has a Scales Arpeggios and Broken Chord book which has different arpeggios in to practice for both hands.

I'd suggest playing them hands apart then trying to bring them together. Try and get use to a two octave arpeggio.
An example of C Major Arpeggio TWO OCTAVE is: -

1 2 3 1 2 3 5 3 2 1 3 2 1 (This is ascending and descending in the RIGHT HAND)
C E G C E G C G E C G E C
5 3 2 1 3 2 1 2 3 1 2 3 5
C E G C E G C G E C G E C (This is ascending and descending in the LEFT HAND)

See how you get on and try to keep your hands low, and your wrists shoulders and arms relaxed.