Worsted cloth is a finer weave and has very little nap (single fibers sticking out). In comparison with non-worsted, it's like the difference between a flannel shirt and a cotton dress shirt. I think the individual threads are also twisted tighter.
If you have ever gone shopping for wool fabrics you may have seen some of the fabric described as worsted, and some of it described as woolen. If you are me, you may have wondered what this meant. Aren’t all wool fabrics woolen? I mean, they are wool, right? Not quite! In brief, worsted and...
There are technical differences and there are degrees of "napness" or "worstedness". Essentially though snooker tables and English pool tables have a nap and need to be brushed in one direction (from the baulk end towards the black spot). "American" pool tables usually, and ideally, are worsted in the sense that they don't have a nap - so the balls behave the same way regardless of the direction they are moving in.
English pool at the professional level has moved towards lightly napped "speed cloths" and is probably headed towards 100% napped cloths (along with a move to "international pool rules") as it suits the game better. The nap is such an integral part of snooker that it will stick around.
Having said all this, I've played English pool on "ice rinks" and American pool on tables where a perfect long pot at a slow speed misses by a full pocket.