I specialize in Twin Flames and soulmates and have been in union with my own Twin Flame for a long time so I'll try to help. Here's most people's general definition.
Union means that the twins have traveled through their respective twin flame journeys and have fully ascended. Ascension is a process through which the soul becomes one with the universe including it's creator. Twins typically ascend simultaneously and encounter each unique phase of the journey and once completed, they achieve union.
Any for all old wounds, inner work, inner or spiritual growth have been completed. Both are fully ascended. Both are fully engaged in their Divine Mission together and in tandem. Any and all old relationships including false twin, catalysts, karmic partners or soulmates have long been completed and satisfied. And as a twin flame pair fully ascended and in union, you likely find it fulfilling to engage in your divine mission (your life calling) together.
For most, since the romantic relationship that twins experience begins as a by product of their mission together, the twins settle into things such as marriage, life partnership, setting up housekeeping together, etc., and behave like any other exclusive romantic couple. If a geographic difference exists, twins have a fantastic way of overcoming issues such as these in order to be together.
What does the Divine Mission really mean? To me, it means "living our own life well as a whole person, ourselves." Our happiness doesn't depend on the relationship we may have with another person, including our Twin Flame - or anyone else for that matter. Our calling, it's everything we do each day. Does that make sense?