The short story is that the APA set up a task force to review the (admittedly scant and old) literature concerning efforts to change peoples' sexual orientation. They did manage to find about 80 old studies, and after reviewing them, found no evidence to suggest that sexual "reorientation" is possible. In fact:
"Contrary to the claims of SOCE practitioners and advocates, recent research studies do not provide evidence of sexual orientation change as the research methods are inadequate to determine the effectiveness of these interventions." Glassgold added: "At most, certain studies suggested that some individuals learned how to ignore or not act on their homosexual attractions. Yet, these studies did not indicate for whom this was possible, how long it lasted or its long-term mental health effects. Also, this result was much less likely to be true for people who started out only attracted to people of the same sex."
That paragraph made me smile ;)
This resolution is extremely important, because there are still a large number of organisations that run or support programs that claim to cure homosexuality.* If someone you know tells you that they're considering patronizing one of these types of programs, please direct them to this resolution, so they at least know what they're getting into.
Many of these programs cost thousands of dollars, not to mention the psychological trauma of being "treated" by someone with no psychological credentials and the guilt of being systematically told that you're sick in some way.
Another reason this resolution is so important is because it was recently found that many therapists in the UK are still under the impression that sexual orientation can be changed in some way, and many have actively helped their patients to try to become straight. Hopefully this consensus will bring an end to this ridiculous practice.
*Actually, a lot of these programs only claim to help you "leave homosexuality" or claim that "change is possible," whatever that means. It's probably just so they don't get sued for false advertising.