probably referring to a diaper with a shell that's part plastic, part cloth-like.
Those usually have a plastic middle area, and clothlike "wings" that wrap around the sides of the hips. Most pull-ups are completely clothlike, but there are a few hybrids of those too.
The clothlike sides help allow your skin to breathe on your hips. (otherwise your skin may get sweaty, itchy, or tend to get pimples - mine does!)
Manufacturing techniques have improved over the years - the first clothlike shells had a high rate of defect that resulted in "pinhole leaks" when wet, so a lot of people just don't trust clothlike shells, but are still looking for the benefits of clothlike wings. (and you can't use plastic for the wings on a pullup) So they prefer hybrid diapers.
There's no actual "cloth" in the "clothlike" though. It's usually a finely woven plastic material, a bit like a furnace filter, that blocks some things (water or dust) while letting air pass through.
A lot of us prefer the soft, smooth feel of plastic on our diapers, that's what we remember from when we were little.
Some of the hybrid taped diapers use velcro instead of adhesive on their tapes. (tykables and bambino do this) The "tape panel" on the front then uses a fine loop material so it also has a clothlike feel to it, although the rest of the shell is still the soft, smooth plastic.
(I've also found that clothlike wings on taped diapers tend to stretch out if worn for several hours, and require a tape adjustment)