The laws of (civil) marriage essentially allows two consenting adults who are not already family members (that is, not related by blood) the voluntary ability to say that they are next of kin and claim the legal rights and fulfill the legal obligations that the law applies to those who are next of kin. This includes - among many things - inheritance, custody of children, medical decision making (should a spouse be incapable), tax and social security. Other laws (divorce) allow the next of kin status to be dissolved.
There have been many cases where the death of one member of a same sex couple has caused the surviving member to be left destitute because in the absence of a will the legal next of kin (typically a parent) has legal claim over the deceased's assets. If a partner is unconscious in hospital then uncooperative parents can prevent that person's same sex partner from making medical decisions and even prevent the partner visiting. I could go on. This would not apply if the partners could legally marry.
Civil marriage is quite separate to a religious blessing. In Australia, a religious minister can perform both the religious and the legal unions, however there is no obligation in Australia for a religious union and marriage can be completely secular. In countries like France, a the civil part of the marriage and the religious part of a marriage are performed separately because of France's rigorous separation of church and state. The overwhelming majority of LGBTI people don't want religious marriages where the religion forbids it, nor the right to marry in places of worship that are hostile to same sex marriage.
John Howard changed the marriage act to specifically state that civil marriage could only be between a man and a woman. Australian law says that LGBTI people aren't equal to other Australians by denying the right to legally nominate next of kin, in the simple legal act of marriage. North America, nearly all of Western Europe, New Zealand and large parts of South America now recognise same sex marriage. Qantas' CEO could marry his partner either in his or his partner's country of origin, but not in the country that they live.