Chores: Jobs you must do in day to day life; cleaning etc. Errand: Usually less general; usually going out somewhere. An errand may be to deliver something or go buy something. Favours: an errand or a chore for somebody else, for example: a friend. Example: "I have so many chores to do today, could you do me a favour and help me clean the house?" (Yana already gave a good answer but sometimes more answers are still useful).

Well chores are usually things you have to do around the house - like cleaning, washing the dishes, laundry or others. Errands are things you need to do usually outside the house - like you need to buy shopping, go to the hairdresser, go to the beauty salon or something like that. Favor is something you would do for someone else. Like when someone asks: Would you do me a favour? - it means that you would do something for them, not necessarily getting anything in return. If you need more help with English don't hesitate to contact me :)