When dragging a card from a backlog to a board (or vice versa), you get the option to add or move the card. Moving is as simple as it sounds, you move the card from its original location to the new one. Adding on the other hand opens up some additional features to gain better overview of your ongoing work.
When adding a card, the card exists simultaneously in multiple locations. This means that any change made to the card, anywhere, will be reflected in all locations. Let's say you are working on an event. The next thing that needs to get done is to design t-shirts. The card has already been added from the backlog to one of the team boards, so when they have completed their part of the task we can add it to the other team's board so they can continue the work.
By adding cards to multiple boards and backlogs, we get an overview of the status of the card, wherever we view it. Learn more about how to make work flow here.
Remember that you can change the default setting for this whenever you by clicking your avatar, Profile and account and Preferences.