To be insane is to be mentally ill. This is also a slang word for acting wacky or wild.
This word has two closely related meanings. People who are insane are suffering from mental illness, which is very serious. When someone commits a crime, it's important to know if they were sane or insane. If they're insane, the penalty is different. Many uses of the word are not so serious. A wild party is called insane, and car salesmen say their prices are insane. A teacher assigning six hours of homework might be told "That’s insane!"