You can move cards and lists within a board and you can even change the board to which they belong. You can also re-order checklists.
The most straightforward way to move a card is to simply click and drag the card up and down in the same list or between lists.
To move a list to a different board, click the context menu in the upper right of the list and then choose “Move List.”
You can also move lists to other boards from the list’s menu. Click on the current board to select the new target board or adjust the list position by clicking on ‘Position’