For the record, the amps on a battery are available amps, not unlike in your home. The voltage is what would damage your components, too little or too much. You're not going to get a 16v battery unless you seek it out. A low or dead batter, under 11.5v can damage things because it's not strong enough to adequately power them.
Amps allow the engine to crank for a long time, run headlights, open your windows... things that get 12v consume amps to do the work. A big heavy subwoofer amplifier still only runs on 12v, but it uses a capacitor to store the amps for when they're needed.
Most electronics in your house are 110-120VAC... and most of them plug into 15A or occasionally 20A circuits... the amp rating dictates how much power can safely flow through the circuit at 120VAC... You can plug you coffee machine into a 15A or a 20A circuit, and it won't notice a difference. Plug an air conditioner and an air compressor into a 15A circuit, and it probably won't last very long.
More amps than what you need will cost more money and take up more room, otherwise more amps are usually more better.