‘Nous’ is the first person plural, so it means ‘we’ or ‘us’. The verb following ‘nous’ will therefore be conjugated in the first person plural. ex: Nous mangeons du chocolat.
‘On’ is used to designate an undefined person or group of person. It is vague: we do not have any information about the number of persons, their gender... A verb following ‘on’ will be conjugated in the third person singular. ex: On mange du chocolat.
In French spoken language you can substitute ‘nous’ by ‘on’, which is more commonly used. However it is better to use ‘nous' when you are writing; it also sounds more formal.