Anyway, so I guess from that you are saying that there are schmitt triggers basically at the pins which are able to apply histeresis so you know that you have, for sure, an input of "0" or an input of "1" to the gates. So it's a pre-configured schmitt trigger which only job in life is to determine if whats at the pins are a "0" or "1".
That's basically it. On gates without Schmitt triggers you can get unpredictable or undesirable results if the input voltage is in that no-no zone between "low" and "high". The Schmitt ensures the gate gets an actual 1 or 0 (high or low) even if the input voltage is out of normal TTL or CMOS spec, say due to noise. They can also be handy for making oscillators and astable/monostable multivibrators, or to measure an analog voltage by timing how long it takes for the voltage to charge a capacitor through a resistor up to the Schmitt threshold (this is sometimes done to achieve a simple/crude A/D conversion with a microcontroller or a timer/counter).