As a noun: 'Act' can be someone pretending - "Don't believe him, it's all an act!" Or it can be a part of a work of fiction - "This is a three-act play." With an adjective, it can also be some form of action - "A hug is a wonderful, physical act." or "It was a really generous act." 'Action' can be something happening, normally something exciting - "There was a lot of action in that movie." It can also be a specific physical movement - "The action of smiling uses less muscles than frowning." 'Activity' can be something happening, normally where things are busy - "There was a lot of activity at the office today." It can also be something that is done - "Reading is probably my favourite activity." or "You should get more physical activity." --- As a verb: 'Act' can mean what an actor does - "He acted really well in that show." Or it can mean behaviour - "He acted inappropriately." Or it can mean to do something or to take action - "He acted quickly." 'Action' can be used as a verb, but it needs another verb with it. - "He took action quickly." or "He sprang into action." The exception to that is in 'corporate' jargon, it's sometimes used instead of 'to do' - "I've actioned that project." or "Could you action those things in the email?" - this is generally regarded as grammatically incorrect and poor English though. 'Activity' is never a verb.