Move topics option allow to move a topic from team to team without losing any topic history: properties, comments...
You created a topic in the "General" team and then created new teams. You want to move your old topic in one of your new teams without losing their comments and history.
Another use case is when you are using team as workflows, one team is for the step 1, another team deal about step 2 and so on. In this case you should use this move topic option regularly.
go to a topic page you want to move
in the contextual menu (available to topic creator) choose the option "Move"
a pop-up show with a selection list of all your project teams
choose the new team you want to move the topic to
the topic is moved
It is not possible to move a topic to another project but from team to team inside the same project
If a project member had access to the topic in the team where it was before and is not part of the new team, he will not have access to it any more. So he need to ask project admin to invite him to the new team.
As teams could have distinct kanban workflows, topic moved to a new team is automatically set to "TO DO" state. So you need to change its workflow state if necessary.