The 's' stands for 'slump'. How wet the concrete is. S1 is prity dry (for laying kerb stones). S2 is wet (for foundations). S3 is very wet (pump mixes).
Colin, a Tarmac concrete batcher.
It should be noted that the concrete should be as dry as practical to enable it to attain the highest potential strength.
Concrete should never be so wet that it flows into the forms like tomato soup. In foundations in particular, you want the best strength you can get, as the entire structure will apply force to them. It should take some handwork with shovels to "ker-chunk" the concrete into the nooks and crannies of the forms. For vertical forms, using a 'stinger' or vibratory device is preferred to settle the concrete into all the nooks and crannies.
A 4" slump is about as wet as you want the concrete mix to be. If you pick up a handful (with gloves) of fresh concrete and mold it into a fat cigar shape, it should hold that shape when you open your fingers. When the concrete mix comes down the chute of the delivery truck, it should stand up on the ground in a little hill, but with some spreading out, too.
For all but the dry structural concretes, you can increase the fresh concrete's slump (wetter) by adding 1 gallon of water for each cubic yard of concrete for each additional inch of slump desired.