S-curve acceleration makes for smoother movements, and can allow for higher speeds.
With conventional acceleration (such as in Mach), motors are accelerated at a continous rate until they hit the required speed, then decelerate at a continous rate.. The transition between accelerating and the required speed is an abrupt change, and and you get some jerk at the transition points.
S-curve counteracts that jerk, by initially slowly accelerating upto max acceleration then gradually reducing acceleration before hitting the required speed. This helps to eliminate jerk, as the transitions are smoothed.
Here's a nice graph showing it I found via a quick google-
Attachment 8040

Look ahead, is where the g-code (or whatever code a Hurco uses!) is read and processed several lines ahead of the current move, so axis movement can be planned in advance and movement smoothed. Nearly all CNC controllers will do this to some extent.
I understand the principle, but it's kinda hard to explain, however Art (original Mach coder), done a good explanation about all these a while back - Yahoo! Groups and the rules he used for Tempest (was a development of Mach3, which stalled for various reasons, but is still available in it's limited form). The post's a bit involved, but he does a good job of explaining the principles and theories behind S-curve, lookahead and smoothing.