This was a popular gearing set-up back in the day when bikes had 5- or 6-speed freewheels and folks wanted triples set up for touring (for example).

In front, you have two chainrings that are pretty close to the same size -- say, a big ring of 52 and a middle ring of 47. Then you have a third chainring, a granny gear that is pretty small -- say, only 24T or 26T.

You then have a freewheel spaced so that each time you change cogs in the rear you are making a "full" gear change, but because the chainrings in front are so close together when you shift between the big and middle chainrings in front you are making a "half step."

So -- if you are quickly moving through the gears, say when you encounter a moderate hill or slowing down, you make big gear changes by shifting to different cogs in the rear. Then you can "fine tune" the gear you want by making "half step" gear changes in front. Finally, for climbing big hills, you drop into your granny gear.

A properly set up half-step triple is (was) a thing of beauty. Because your two big chainrings in front were only about 5 teeth different, your shifts in front were really smooth. You sometimes had to make double shifts (make a big shift in rear, and then fine tune in front), but the shifts were easy to accomplish. There was a big gap between the middle chainring and the small chainring, but since you only used the granny gear when encountering a big hill, that was not such a big deal.

Back in the day, I had two touring bikes set up this way, and I loved it.

As I understand it, the need for half-step gearing pretty much went away when rear cassettes starting coming in 8, 9, and 10-cog versions.