In biblical times, the idea was for Adam and Eve to take care of the garden and NOT do what they were clearly instructed not to do. After they sinned, Tikkun Olam was meant for bringing it closer to the harmonious state for which it was created.
In the Mishnah, the term Tikkun Olam is used as the motive behind social legislation meant to improve upon society. That means building homes and families, and creating a civil society filled with deeds of caring and compassion, sustained by justice, integrity, and peace.
Today, the term is often used around social policy issues and safeguard of those who may be at a disadvantage. Furthermore, Tikkun Olam has become a synonym to the notion of social action, Tzedek (pursuit of social justice), and environmental awareness as a mission for every human being.
Another take is that Tikkun Olam implies that while the world is innately good, its Creator purposely left room for us to improve upon His work.