« se dérouler » is used in the figurative sense, which implies un underlying metaphore; however it’s a set metaphor, rather stricly defined by the dictionaries, not what we mean usually by “metaphor”, that is the often unique use by an author of a term or phrase in place of another in order to create a special effect, that to which is given the more familiar term “figure of speech”. In this figurative sense, using a quite nicely coincidental English word in a figurative way, it means “to unfurl”; this term is however litterary. A much less metaphorical rendering, but proper for everyday use would be “to go”; thus you would keep to the mind of the French by translating it “My day went well”. The reason for saying “ma journée s’est bien déroulée” rather than for instance “ma journée s’est bien passée”, that latter being possible if the former is (it “covers” it so to speak), is that you might imply an unusual and rather formal activity that was to take place during that particular day, but such fine distinctions can be commonly disregarded.

Le dictionnaire Petit Robert n’indique pas une métaphore, mais un usage figuratif pour la forme pronominale :

Se dérouler : prendre place dans le temps, en parlant d’une suite ininterrompue d’événements, de pensées.

… Synonymes : s’écouler, se passer.

Cela ne ressemble pas à la définition de la métaphore, car le mot figuratif englobe l’analogie, mais pas la notion de style littéraire ou poétique.