If someone says you are
mad as a hatter, they are accusing you of being quite irrational. The sense of madness here is "suffering from a disorder of the mind; insane." This phrase usually refers not to someone who is actually insane, but rather to a more normal person who is behaving in an irrational
way.
The phrase emerged in England in the 19th century. Hatmakers in those days used a lot of felt that was treated with chemicals including lead, arsenic, and
mercury.
Unfortunately, those chemicals are highly toxic. The symptoms of such poisoning include palsy, confused speech, and distorted thinking.
Today, making hats is a much safer profession, but the phrase survives.
An
interesting alternate explanation of the phrase derives hatter from Anglo-Saxon atter (poison), which is related to adder (a poisonous snake whose bite was thought to cause insanity).
