Social constructionists believe that although same-sex love has occurred in all cultures, the concept of certain people being predisposed to love only one sex (and thus being "homosexuals" or "heterosexuals") is an inaccurate concept invented by modern Western society, and does not accurately describe how human sexuality develops in other cultures. They believe that a person who describes themself as homo or hetero and orients their sexual behavior toward only one gender does this only because their culture has fed them certain ideas about sexual identity.
Essentialists believe that the concept of people being "homosexuals" and "heterosexuals" accurately reflects an unchangeable reality which holds true for all cultures in all of history, and thus that a person's homosexuality or heterosexuality constitutes an unchangeable "essence" rather than a socially constructed characteristic.
People who believe sexual preference is always inborn are pure essentialists. People who do not believe anyone is born with any predisposition toward any particular sexual preference are pure social constructionists. There are also many people who are somewhere in the middle and agree with certain aspects of both social constructionism and essentialism; they may believe that there's some degree of biological influence on sexual preference but that cultural ideas also have an important influence. Queer by choice people are by definition not pure essentialists, but not all of us are pure social constructionists either (although a lot of us are).
In their efforts to fight homophobia, essentialists tend to start with the assumption that queers will always be in the 10% minority and that heterosexuals will always be in the 90% majority. Essentialists typically try to promote queer rights through arguing that gay people "can't help" being queer and saying that giving queer people equal rights to marry and not be discriminated against will not cause anyone else to become queer.
Social constructionists tend to believe that in a truly liberated society where same-sex desire was not stigmatized, everyone would feel and acknowledge feeling same-sex sexual desire, and exclusive heterosexuality would fade out of existence. Thus, they believe that in order to win queer rights we have to also teach hets to liberate their own queer potential. Social constructionists typically try to promote queer rights by talking about other cultures where all members of the society were expected to have same-sex relationships, and by asking hets to imagine that they'd grown up in a society like that, and by trying to get hets to face and accept their own queer potential and see same-sex desire as a natural part of what all humans are capable of experiencing.
Essentialist queer activists typically get mad at social constructionist queer activists for being too threatening to hets by actively trying to convert hets to queerness. But social constructionist queer activists typically get mad at essentialist queer activists for making hets too comfortable, agreeing with too many het ideas and not challenging het people's deepest fear of their own queer potential.