It kinds goe slike this, If you have an amplifier with a gain of 2, then 10 mV may become 20 and 0.5 V may become 1V, but a 10 V input may not become 20 V because the supply is limited to 15 or so. In this case any input >7.5V clamps the output at 15 V. (simplified)
There are other types of overloads too, like the common mode voltage is exceeded, but lets not look at that just yet.
Another way to say the "input is overload" is to say the "output is saturated" or at the maximum.