Half step is a gearing progression such that a shift on the front derailleur was half the difference of a shift on the back. It was useful in the days of five speed freewheels. Many freewheels back then required a 17 tooth second cog so, to get any kind of sensible gear progression in back, you had to have a pretty wide ratio freewheel (14, 17, 20, 24, 28). With that kind of freewheel and 52/42 chainrings (called alpine gearing back then), your two fastest gears would be 83 and 100 gear inches. that's a pretty big gap. With 52/48 chainrings (half step gearing) you'd progress from 83 to 92 to 100 gear inches but you'd have to constantly shift your front derailleur to get the next gear in the progression.

Modern gearing systems with 8 or 9 relatively closely spaced gears on the back have eliminated the usefullness of half step gearing.