Le Cordon Bleu refers to the blue ribbon used by the Order du Saint-Esprit (founded by François 1er, I think). The Order was established to compete with the Order of the Garder & the Order of the Golden Fleece. From the ribbon was suspended a medallion of the dove of the Holy Spirit descending upon a gothic cross. The Order was restricted to the very wealthiest & best connected in the nobility and became associated with sumptuous food, drink & clothing. The cooking school open in 1895. It continues to operate in Paris and (since abou 1990) 10-15 other cities around the world. It is owned by the Cointreau family, as in the orange liquer.
Just to add to the previous explanations, "cordon bleu" is actually used as-is in English, so there isn't a specific translation, although "gourmet cook" conveys the correct meaning. So you might actually say
She's no cordon bleu chef
A real cordon bleu cook