AprilComes+like+an+idiot,+babbling+and+strewing+flowers.

April does not actually come babbling, so it may be assumed that Millay is referring to another party. Babbling is something that is associated with children learning to speak. She might then be insinuating that she does not understand those that would come foolishly speaking, "strewing flowers" of happiness when the world (as described in previous lines) can seem so bleak.