That explanation is Succinic acid, baltic amber is known to contain between 3-8% succinic acid. According to proponents this is released from the beads and into your baby. The succinic acid then allegedly has an analgesic effect and so reduces the pain of teething. Here is where my first point regarding plausibility comes in:
Amber is tough, really tough. This is a material that has persisted for thousands and in some cases millions of years unchanged. Suffering through heating and cooling of innumerable climatic changes through the years. Yet this same tough unchanging material with happily give up its chemical components upon the gentle heating it receives on being placed next to your babys skin? Colour me unconvinced[1&2]. Related to this point amber has a hardness on the Mohs scale of between 1 and 3 [3], baltic amber which is usually touted as the therapeutic variety (because of the high succinic acid content) is at the high end of this scale 2 2.5. To put this in perspective, Tin has a hardness of about 1.5 and Gold is 2.5-3 [4]. But forget about this point, I dont need it. Lets say for argument sake that clinically relevant amounts of succinic acid are released by the amber and absorbed by your babys skin.