A couple can choose to "break" their marriage in Orthodoxy.
Likewise, a priest can be devested and is no longer a priest.
In RCC, nothing sacramental can be "broken," so the justification is that the marriage never really happened.
Likewise, a priest who is de-vested is still a priest, just unable to serve.
So, the Orthodox stance is a little different. We dont claim "annulments," but instead recognize the broken condition of the individual and couple. Like any of our broken conditions, it requires repentance with regular confession to receive Communion, and there may be a blessing granted for another marriage depending upon the individual--but then, if both parties are marrying for a second time, much counseling is given and the service itself is different, containing more penitential prayers. There is never a blessing granted beyond 3 marriages--which would have to be a pretty special situation, but could happen, especially in situations dealing with widows and widowers who didn't necessarily end the earthly marriage by choice.