Sexual Orientation is the term used to describe what gender(s) (or other possible distinctions, such as race(s)) one is sexually attracted to. A person's sexual orientation is usually the deciding factor in what title they take on or have placed on them.
If one is attracted to the same gender as themselves, that is referred to as homosexual, if one is attracted to the opposite gender, they are described as heterosexual, and if one is attracted to both, they are commonly referred to as bisexual  or pansexual. Many people do identify as something else, such as Demisexual (attraction to people because of emotional connection) and Asexual (lack of sexual attraction), plus the umbrella term Queer is used to describe people who don't quite conform to any specific label.
There is much controversy  regarding how and why people "become gay." The typical religious (Christian) perspective on the issue is that people are able to choose their sexual orientation, so that if one wanted to be gay, bisexual, or heterosexual, they could become so by willing it. 
The opposing viewpoint usually states that people are born with a certain predisposition to a certain gender, therefore it is beyond the person's control as to who they're attracted to.  Thus the phrase, "born gay" came into existence. Furthermore, the disagreement on this question can be seen on almost any blog or forum in which the discussion has been brought up.