Yes, you can move Folders as well as individual Documents in the Library using the instructions listed in this article.
Moving Folders:
Method 1:
Click on the Folder that you want to move to view its contents.
Hover your mouse over the title of the Folder and click the ellipsis icon that appears in the top right > Move.
You'll then select a new location for the Folder from the dropdown menu. 
Method 2:
In the Folder Tree Navigation located on the left side panel of the Library, hover over the Folder that you want to move and click the ellipsis icon on the right > Move. You'll then select the Folder's new location from the dropdown menu (see the above screenshot for reference).
Moving Individual Documents:
Method 1:
Hover over the Document that you want to move and click the ellipsis icon on the right > Move.
You'll then select the new location for the Document from the dropdown menu.
Method 2:
Hover over the Document that you want to move and click the ellipsis icon > Edit.
Use the "Folder Location" dropdown menu on the File's Details Page to move the Document to a new location.
Method 3: (Allows for moving multiple Documents at once)
Hover over a Document that you want to move and select the checkbox that appears in the top left corner. You'll then have the ability to select checkboxes for other Documents on the page.
Click the "Actions" button after making your selections > Move. You'll then select the file's new location from the dropdown menu.
You can also use this method in the Document Report to move Documents in bulk. You can access the Document Report, which includes a full list of all Documents within a specific Library, by hovering your mouse over the Library's header > Reports.
You'll then click on the Document Report.
Switch to the "Table Layout" to view the Documents in a list format.
Select the checkboxes next to the Documents you want to move or click the top checkbox to select all items in your view > Actions > Move.
FAQs
Are the Folder's contents moved along with the Folder?
Yes.