Basically, if this proposed equal marriage legislature goes through, it will mean that a gay couple can adopt as a couple, instead of each of them having to adopt separately. Also, they will be able to take the other one's name when they get married instead of changing it later separately. And, instead of having to check the "Registered relationship of two persons of the same sex" box on a form, they can check the "married" box. All this would lead to lighter bureaucracy.
Issues that will still remain after this is for instance a case where a gay couple uses a donor they know to conceive a child, and want that donor to play a part of parent in the child's life. According to Finnish legislature, a child can not have more than two parents. So either one of the people in the gay relationship has to give up his or hers parental rights, or then the donor has to give up his or her rights.
One issue the changed legislature would bring is that gays will no longer be able to use the "Sure, I'd love to marry you, but it just isn't legal" argument with their spouses anymore
But I haven't understood how gay marriage threatens a heterosexual marriage either.