Happiness is all about yourself. When you feel that you are happy inside then you'll definitely try to spread the happiness among your closest persons.
Indeed. Happiness is what a person feels within Him/Her. And to make the person even happier, He/She will spread it to other people. A good situation to explain The quote "Happiness is real when shared" is when a person doesn't feel happy being alone anymore, if He/She doesn't feel happiness within His/Her material possessions. And that to satisfy Him/Her happiness He/She needs other people accompany and be happy with the person.