"Ex-gay" is a term used to describe people who claim they were once GLB, but have changed their sexual orientations to be heterosexual. Telling people they can change their sexual orientation when this is not possible, promotes anti-gay feelings and hostilities.
You might have heard people say things like, "If a gay person really wanted to change, he could." Or, "lesbians just had bad experiences with guys. All they need is to meet the right one. Then they'd be straight."
Despite what people think, being GLBT is not a choice, and it is not something that can simply be changed through force of will. Though it is true that people can change their behavior, that's not the same as changing their sexual orientation. For example, a gay guy might decide to date girls because of social and family pressure, but that doesn’t mean he's no longer gay.
Occasionally, parents of GLBT kids think that something called “reparative therapy” can make their children straight. Though there is very little evidence that reparative therapy does what it claims, there is plenty showing the emotional harm that it can inflict.
The "ex-gay" movement is often related to particular organizations (some religious, some not) that have anti-gay agendas and policies.