You could use this sentence in any context where someone can stand as you, express your ideas to a group, etc. Of course, the lawyer example is clearly one. But there are many others: such as going to an assembly where votes take place, if you can't go, you can send someone who will "represent" you. The French political system is a «démocratie représentative», where some elected individuals represent the people (or so we are told... but that's another subject! :p ).
Actually this is a good point. A narcissist could stand in front of a painting of himself, showing it to his guests, saying: « Il me représente ». Although as it is, it wouldn't be used much, we'd need something else after it, like : « Il me représente défiant mon plus terrible ennemi ».
The object pronoun for "je" is "me" and it has to be placed before the verb: il me représente
"moi" is a stressed pronoun you can use after prepositions (de, par, pour, sans, etc.) but not "à" if the verb is naturally constructed with the preposition "à":
- il chante avec moi = he is singing with me
- il part sans moi = he is leaving without me
- parler à = il me parle (indirect pronoun) = he is talking to me
- donner quelque chose à quelqu'un = il me donne une pomme (indirect pronoun) = he is giving me an apple.