If you say someone is wearing a tin foil hat, it's a sarcastic or mocking way of saying they're being unreasonably paranoid. The joke is that they think the government(or maybe aliens) has the technology to read minds, so they wear tin foil on their heads to block the mind-reading rays.

It's an idiom, it became common in my lifetime, and I'm not sure how it began. Wikipedia says that "caps of metal foil" were mentioned in a famous 1927 science-fiction story. It can be an insulting way of saying somebody is crazy. It can also be a joke about one's own fears. "It's strange that I started to see Internet ads for ski areas just after I bought skis in a store. Maybe I need to put a tinfoil hat on, but I think that store must have sold my information to someone." In the mental illness called "paranoid schizophrenia," people often believe some hostile power is controlling their minds. In the old days they would probably have said they were possessed by demons. Around 1900-1950 the general public became aware of "rays" (X-rays, gamma rays, etc.) and I suppose paranoid delusions changed. Around 1910 or so, Robert Service wrote a terrifying poem in which the speaker, going crazy in a cabin in the Arctic, decides to kill his partner because he thinks his partner is "shooting electricity into the walls." The public also became aware that metal can shield against some kinds of radiation. "Tinfoil hat" is strange language because "tinfoil" is an outdated word. During my lifetime, in everyday life, the only common metal foil has been aluminum foil.