Your client does not support opening this list with Windows Explorer.
Whenever we face such kind of issues, one thing should be important that you have already installed a valid copy of Office application on your client machine becuase Explorer view is windows feature provided by means of sharepoint that uses client functionalty i.e. Office 2010
-As per the SP 2010 functionality, ensure you have Office Professional PLUS installed on your client machine.
-Integration features of Office client Applications and SharePoint uses WebClient service running on the client machine.
The problem where i faced this problem was belongs to OS-Windows Server 2008 R2. So i started searching for this WebClient Service to see if it was running or not. I went to Start
->Administrative Tools->Services i browsed through all the services but could not find it.
Generally, we found this service in services console but the mystery became complicated and i started exploring the features of Windows Server 2008 R2......n yes, i got it !!
The name of the feature which supports this functionality called as Desktop Experience.
Note: The WebClient service is installed only when you install the Desktop Experience feature on you Server 2008 machine.
Here are the steps that i have taken to resolve this issue:
1) Go to Start->Administrative Tools->Server Manager
2)In Server manager Click on Features and the click Add Features
3)Select the Desktop Experience Feature and install it. Then Restart the Server (Required for installation of the feature)
4)Go to Start->Administrative Tools->Services
5)Select the Web Client Service and Start it.
I hope, the above information will helps you to resolve your issues...
Please let me know in case of any issues,Thanks !!