Marriage is a contractual agreement between two people to support and rely on each other in all intimate and personal matters. It is of great practical value to have such a person in your life, and your mutual achievement of happiness is greatly aided by such an arrangement.
The marital contract itself legally protects both parties should anything go wrong, and guarantees they have the needed rights and privileges to fulfill their contracted obligations. Because people who make such agreements together are often more stable and reliable and productive, and thus as a unit of greater benefit to the state and the community (particularly, but not only, in the successful raising of children), the state often supports such agreements by providing married persons an array of benefits.
These facts entail several concurrent reasons to get married (provided you find someone enjoyable, loyal, and trustworthy enough, as generally only those who love you are): to receive the state benefits afforded to the married; to receive the benefits of having someone to rely on in living your life, who likewise has all the socially and legally recognized rights to look after your interests as diligently as you look after theirs; to enjoy the security of an intimate partner (not just sexually but more importantly in the sharing of secrets and advice); to ensure security against loneliness (as one of the purposes of a marital partner is to always be there when you need them and to share experiences with and build a life together); to make your life easier and more productive by sharing resources and incomes and dividing the labors of life between you; and, if you wish to have children, marriage extends all these benefits to their welfare as well (ensuring a stable and productive environment of financial, physical, and psychological security, of divisions of labor, shared resources, and state benefits), and is therefore of paramount value to the goals of any parent.
In short, to have a spouse is to have an assurance of security against loneliness and abandonment, to share the joys and difficulties of life with a consistent partner whom you can grow to know exceptionally well, and to secure all the external and internal benefits of being socially recognized as a committed couple. Though these assurances can never be a guarantee (as people must be free to divorce to escape a bad marriage, for marriage is only of value if it is conducive to overall happiness), a couple willing to undergo a marriage, in ceremony and contract, has established a willingness to the commitment that is by definition more secure than in the case of a couple unwilling to undergo these things. This greater proof of commitment not only brings each other greater confidence in their situation (and a sense of security is essential to human happiness), but this exceptional commitment then also receives the recognition of the state and community. And this is recognized through public symbols, such as the wearing of distinctive rings or the sharing of names, and the filing of official documents.
A successful marriage, therefore, is one that best realizes all of these goals, such that an unsuccessful marriage is one that does not realize them or does so unreliably or inconsistently. To achieve a successful marriage requires selecting a spouse with great care, with an eye toward their ability to realize a successful marriage with you, and this generally requires some degree of genuine love for each other (as no other bond of attachment is as enduring at all levels of required commitment). But by "love" in this context is not meant passion or elation, but an exceptional degree of admiration and compassion. And maintaining a successful marriage requires revisiting all the mutual requirements (in terms of obligations and expectations of both partners) and managing their fulfillment rationally.
Given these facts, marriage in no sense requires any particular gender model. Gay couples can realize all of these goods just as well as straight couples can, even to the extent of raising children, and in fact as human happiness is greatly benefited by a good marriage, it is unconscionable to deny gay people access to it. Marriage could even in principle be developed as a nonsexual way for single parents to improve their own happiness and the happiness and welfare of their children, by enjoying all the contractual benefits of marriage, and simply foregoing the single component sexual fidelity (and replacing that instead with well-grounded rules governing appropriate conduct of their mutual sex-lives). In this way even straight same-sex couples should have access to marriage.
(On the issue of marriages of more than two people see the related question on this website about polygamy.)