A Schmitt trigger input standard allows input buffers to respond to slow input edge rates with a fast output edge rate. Most importantly, Schmitt triggers provide hysteresis on the input buffer, preventing slow-rising noisy input signals from ringing or oscillating on the input signal driven into the logic array.
The following voltage diagrams illustrate the difference between the Schmitt trigger input standard and the LVTTL/LVCMOS input standard, and how Vschmitt relates to VIH and VIL.