Holding down the alt or shift key allows you to select multiple cards for edits and movement.
When using multiselect, a banner will appear at the top of the page showing you how many cards are selected and what actions can be performed on them, selected cards are also highlighted with a blue border. Apart from regular movement, you can also archive, assign, tag and delete the selected cards. You can exit this mode at any time using escape or clicking the X symbol to the right in the banner.