You can map a network drive for SharePoint Online by adding a network location within a Windows environment, to achieve this please follow the steps below.
Login to https://portal.office.com and check 'Keep me signed in'
Press the Menu button in the top left hand corner, and then 'Sites'
Select the site you wish to map, i.e. 'Team Site'
Now select the 'Documents' Library from the navigation bar
Select the 'Library' tab from the top, and then 'Open with Explorer'
Copy the URL within the Explorer Window
Select Start and right click on 'This PC' or 'My Computer'
Select 'Map network drive'
Select the option to 'Connect to a Web site that you can use to store your documents and pictures', and press Next
Select 'Choose a custom network location', on the new window enter the URL of the documents library that was previously copied and press Next
Enter the name you would like to give the mapped drive, select 'Next' and 'Finish', the drive will now be mapped.
Apple OS X
To successfully map a SharePoint drive for Office 365 on a Mac, you will need to download the free Document Connection for Mac tool provided by Microsoft. This tool should be included within Office 2008 or later however is only supported in OS X version of 10.9 and above.
Open the Document Connection Tool, select 'Add Location' in the top left hand corner and then 'Connect to a SharePoint Site...'
Enter your SharePoint URL into the Address field by copying and pasting this from a web browser. Select an Authentication type 'Forms-Based' and then click 'Connect'.
An Office 365 authentication window should now open, enter your Username and Password and sign in. The site should now be available within the Document Connection tool.