Andar conmigo literally translates to "walk with me". However, in many Latin American countries, particularly in Mexico where Julieta Venegas is from, the verb andar is frequently used as a colloquial way to express dating or being in a romantic relationship.
The entire song revolves around this beautiful double meaning. When she asks, "Dime si tú quisieras andar conmigo", she is metaphorically asking if this person wants to travel down life's unpredictable paths with her, while simultaneously asking them to be her romantic partner. It is a brilliant, poetic, and highly culturally relevant phrase to learn.
Mexican pop star Julieta Venegas wrote one of the most direct love proposals you will ever hear in Spanish. The whole song rests on a charming Mexican phrase: andar conmigo. Literally, andar means "to walk," but in Mexico and Latin America, andar con alguien means to date or go out with someone. She plays with both meanings at once. When she sings Hay tantos caminos por andar ("There are so many paths to walk"), she immediately follows it with the big question: Dime si tú quisieras andar conmigo ("Tell me if you would like to go out with me").
There is no awkward beating around the bush here. She sits down with her crush and asks them to skip the games: No te asustes de decirme la verdad ("Don't be scared to tell me the truth"). She is ready to trade old secrets and lay her entire life story out on the table (Estoy ansiosa por soltarlo todo - "I'm anxious to let it all out"). Even if the answer ends up being un siempre no ("a forever no"), she thinks sitting together right now is reason enough to celebrate: Festejemos que la vida nos cruzó ("Let's celebrate that life crossed our paths"). It is honest, cheerful, and refreshingly bold.