SQL Server 2008 R2 Setup Client Tools Connectivity During SQL Server 2008 R2 setup I see a checkbox for "Client Tools Connectivity" and "Client Tools Backward Compatibility" installation options. It says these are component for client server communication. Can anyone explains what are these components? What is being actually install on the server when you choose these components.
The client tools installs things like sqlcmd, odbc, db-lib, SMO (SQL Server Management Objects), AMO (Analysis Server Management Objects) etc; the backwards compatibility tools includes wrappers for COM objects such as DTS, STrace, osql etc... These tools can help you in various tasks depending on your need - and in some cases may be mandatory depending on what you are doing. 

They can also be required when applications have been written that use them to connect to SQL Server - as such they are available as redistributables. You may not need all of them installed and so you should think about what you really need before installing them as extra components increase the surface area of attack upon a system.

For more information about these options please see the following link:

http://technet.microsoft.com/en-us/library/ms143786.aspx

I hope this helps you.