The description is of the chain width. There's quite a lot of history, but the short answer is "they make chains narrower to fit more gears in".
In order to fit more rear sprockets in without making the rear wheel ludicrously wide manufacturers have crammed them closer together. To make that work they've made the chain narrower, limited mostly by material strength (for a given cost and manufacturing complexity, anyway). One consequence of this is that front chainrings also have to be narrower, but there's enough tolerance there that you can usually run a chainring one step wider than ideal and get away with it. Running a narrower chainring than you need will almost always work, but since they're usually more expensive that's not often done (except for people running 7 speed setups where the cheap chainrings are 8/9 speed these days)
Most chains are the same length when sold, with extra links discarded when the chain is fitted. Most bike shops have a bin of those offcuts and use them to replace broken links or if someone is especially poor they can stitch together a full chain out of the bits (it's very slow and many modern chains are not designed to be assembled without special joining pins). The problem is for people with folding bikes that often have longer than usual chains, as the standard size is frequently a few links sort of what they need. Recumbents obviously suffer from this to an even greater degree, taking between 2.5 and 3.5 chains. SRAM and others sell chain in rolls which mitigates this problem, but obviously you'd need to be using a lot of chain to justify buying it 100m at a time.
Wikipedia has a useful description and link to more detail. Key info:
- 6 speed - 7.8mm (all brands)
- 7 speed - 7.3mm (all brands)
- 8 speed - 7.1mm (all brands)
- 9 speed - 6.6 to 6.8mm (all brands)
- 10 speed - 6.2mm (Shimano, Campagnolo)
- 10 speed(Narrow) - 5.88mm (Campagnolo, KMC)
- 10 speed(Narrow, Direction) - 5.88mm (Shimano CN-5700,CN-6700,CN-7900)
- 11 speed - 5.5mm (Campagnolo, KMC, Shimano CN-9000)
