The stock alternator and battery meet the electrical needs of your car’s stock features, and that’s about it.
The draw from a big* audio amplifier – combined with regular vehicle features – runs your battery down faster than the alternator can charge it. This causes the voltage to drop.
Voltage drops damage amps.
Think of it in terms of paying rent. You need $1000 per month for rent. Your bank account (batteries) has a certain amount of money you can use to pay rent to your landlord (amp). You also have regular expenses (lights, stereo, AC).
To keep money in your bank account, you need a job that pays enough money (current) to keep money in the bank. If your job doesn’t pay enough, your bank account is going to run out eventually. You either need a cheaper place (smaller amp), a better job (higher output alternator), or a big bank account (more/better battery capacity).
*A “big” amp is anything over 1000 W RMS. Smaller amps are often able to run on a stock electrical system, but upgraded charging never hurts!