Creon has just recently convinced Antigone not to die. However, Creon continued to talk and it was this metaphor that caused Antigone to revert back to her goal of dying. By comparing life to happiness, Antigone was able to realize that Creon's version of what "happiness" represented was different to her own. This engages the audience because although (due to the elements of a tragedy) they know that Antigone will die, the glimmer of hope that she may live keeps the audience on edge. However, when she changes her mind and chooses death over life once again, the audience despairs.
The metaphor also characterizes Antigone. She is not one to be happy being told what to do, however that is inevitable in her life that is all planned out. Thus, she is unable to be happy in the life that she lives, but if "life is nothing more than the happiness that you get out of it", as Creon states, she can not have a life.