A folie a deux is a mental disorder that two people share and experience at the same time. If you and your best friend are convinced that her dog can speak English, it may be a folie a deux.
When two people have the identical delusion — believing something is true which clearly could not be — it's called a folie a deux, or sometimes a "shared psychotic disorder." This unusual disorder is more likely to occur in a closely related pair, like twins, or a married couple, who are isolated from other people. Folie à deux means "shared madness," or "madness for two" in French. If three people share the delusion, it's a "folie a trois."