Columba keeps mail in folders. You start out with a few mail folders, such as Inbox, Outbox, Drafts, Templates, Sent and Trash, but you can create as many as you like.
Create new folders by selecting Folder->Create new Subfolder... Columba will ask you for the name and type of your new folder, and will provide you with a folder tree so you can pick where it goes.
When you click OK, your new folder will appear in the folder view. You can cut/copy/paste messages between your folders. Alternatively you can use the Move Messages button or Copy Messages button in the toolbar.
You can also use drag and drop to copy/move messages between folders.