You might want to backup contacts on Windows Phone 8 sometimes If you got another new phone or you just want to use another phone temporarily etc. You may also want to transfer contacts If you want to change your Microsoft account you use on your Windows Phone.
On Windows Phone 8 like Nokia Lumia 920, 820, 810, HTC 8X etc, You use Microsoft account like hotmail, xbox, outlook etc accounts to set up your phone for the first time. Windows Phone automatically syncs contacts, email, calendar between your Phone and Microsoft account. So your Microsoft account contains all contacts etc.
If you reset your Windows Phone and use the same Microsoft account to set up the Phone again, Your contacts, email etc will be synced to your Phone. If you want to restore other data like apps, videos, photos etc, You need to turn on backup option on Windows Phone.
How to backup contacts on Windows Phone 8 like Lumia 920, HTC 8x etc
1. Easiest way is to export contacts from your Microsoft account. Your Microsoft account contains all contacts. Using browser on your computer, Go to Microsoft email account like Outlook.com, Hotmail.com, Windows Live Email sites and sign in with your account username & password.
2. Click on the arrow as shown in the above image. You will get a drop down. Click on People.
3. People page contains all your Windows Phone contacts. Click on Manage menu and select Export to backup all your contacts to a CSV file. CSV file will be downloaded to your computer.
If you prefer to have all your Windows Phone 8 contacts sent in email in a text format, You can download Contacts Backup app from Windows Phone Store.
This method works on Windows Phones including Nokia Lumia 920, 820, 810, 822, 620, HTC 8X, 8S, Samsung Ativ etc