Looks like an amplifier. ADS, too. They use to be real good. I haven't seen an ADS product in a while.
If you've got an ipod at home, and a headphone-t0-rca (the red & white co-ax audio) connections, you can connect it to the amplifier ... you'll need power from the battery, too. Amplifiers and radios generally have a "turn-on" or "remode" lead. The generic color code would put that at a blue wire behind the deck (or a blue wire to the amplifier). This wire allows the power wire to stay connected, and the turn-on wire is connected to the ignition - so that you have to have the key in and turned on to turn on the radio/amplifier. On a boat, most people use a switch for the remote wire. This way you can flip the switch on while you're anchored and on the beach and use the radio. The only down side is that it's possible to leave the radio on even when you take the keys out. - I've heard people trailering down the road with the boat still blasting tunes.
Based on the physical size, next to that speaker grille, there doesn't need to be another battery. My first guess was that the amplifier runs the subs and the mids and highs play from the head-unit ... but on second look, there appears to be a front and rear set of rca wires plugged in (lower right of amplifier). The blue, red & black wires on the left are power (red), ground (black), and remote/turn-on (blue).
Alpine is a great product. Especially for head-units. To check the amplifier, you need 12V power, and an audio signal source on the RCA outputs (here's where you can use your iPod since the face is missing from the deck) ... the speakers appear to be connected already. If you're using your iPod with a headphone adapter, you'll hear the music loud and clear with the amplifier. If the amplifier is not working, you'll still hear music, but not well - the amplifier in the iPod doesn't have the power behind it to push a full-size speaker.