This is the percentage of the surfactant as presented – liquid or solid – that is the actual surfactant. For instance, a bottle of Cocamidopropyl Betaine (CAPB) may have an active surfactant matter or ASM of 30%. This means for every 100 grams of CAPB you buy, there will be 30 grams of active surfactant matter.
Read a much longer post on this topic here: A quick look at active surfactant matter (ASM)