Animal dissector is a skill associated with the animal dissection labor. Animal dissectors make extracts from certain caged vermin, either fire snakes, cave spiders, or phantom spiders, at a butcher's shop, stored in a suitable vial. The skill level of the dissector determines the speed at which the labor is completed, and the quality and material of the container used adds to the value of the final product. The vermin themselves must be caught in animal traps by trappers, and do not survive the extraction process.
Animal dissection (along with the similar fish dissection skill) is only marginally more useful than cheesemaking in the current version of Dwarf Fortress. The vermin the skill targets are one of many such species that trappers may catch, making them difficult to source in any applicable volume as there is currently no way to specifically target trapping jobs. Dissecting a fire snake produces liquid fire, a trade good which is produced in stacks of five and worth a not-insignificant 500☼ in total; the other vermin produce venom, which unfortunately cannot be applied to weapons and thus also serves as a (less valuable) trade good.
Once alchemy is implemented (and trappers are made to target specific species, and poisons are made to be reliable in weapon application), animal dissection will likely become a more useful skill for your dwarves to have.