This can be made much simpler. IDEAL amplifiers swing rail to rail. This means they can take a small signal and take it all the way down to their lowest voltage or all the way up to their highest voltage (these are the +/- voltage supplies that are connected to the amplifier). Now, that's the ideal case. Transistors can never actually output EXACTLY that highest or lowest voltage due to leakage current. For example, we can just say this: If we have an amplifier that is connected to a +/-15V supply, it'll be able to output up to +/-14.7V. When your amplified signal tries to go past the 14.7V limit, clipping occurs. Generally, that extra voltage drop is due to something called threshold voltage.

As Ernie said, these amplifiers have fixed gain, so the max value you can input will always be in terms of voltage. Also, most Audio Amplifiers have FET inputs meaning they have infinite input impedance and no current flows in (ideally no current, there is always leakage), therefore this value will never be a maximum in terms of current.

Ernie is right, however, on loading the amplifier with a low impedance. Ideal amplifiers have 0 output impedance. Since you're always loading an amplifier in parallel, whatever load will be in parallel with 0 ohms which can then be approximated as ~0 load. This value is actually closer to ~10 Ohms for good amplifiers and ~100 Ohms for the crappy ones. If you load an amplifier with something that is less than its output impedance, you'll generally get distortion due to higher current draw.

The conversation past here gets very complicated. Audio amplifiers (talking down at the IC level here) have multiple stages, each designed for a specific purpose. The Class A,B,C, AB, etc. amplifiers we all know of represent the output stage, etc.