I am planning to upgrade AEM 6.2 to 6.5. There is a section called 'Prior to Future Upgrade' in Common Repository Restructuring in AEM 6.5. Does it means do we need to perform these Prior to Future Upgrade activities?
When upgrading to AEM 6.5, a large subset of the content under /etc will be duplicated in other folders in the repository. These new locations are the preferred locations in which the content is referenced. However, every attempt has been made for the AEM 6.5 upgrade to be backwards compatible with the previous locations in the /etc folder and so in most cases the old locations will continue to be referenced by AEM code until changes are actively – and in many cases manually – made in a customer’s application.
AEM 6.5 code will continue to reference the old locations until the modifications are implemented as part of a customer release. While there is no forced timeline for which the changes should be made, it is recommended that they are made before the future upgrade since future features may rely on the new locations being referenced.
I assume that you are referring to this documentation  and the following bullet point on that page:
"Prior to future Upgrade - the vast majority of the /etc restructuring changes can be deferred until some time in the future post-upgrade. As previously mentioned, AEM 6.5 code will continue to reference the old locations until the modifications are implemented as part of a customer release. While there is no forced timeline for which the changes should be made, it is recommended that they are made before the future upgrade since future features may rely on the new locations being referenced. Also, documentation for a given feature will by convention reference the new locations and it could thus be confusing if the old locations are still being used."
As @Bhuwan_B already quoted from the same documentation page, the system will take care to duplicate the content: it will leave everything under /etc for compatibility reasons while also copy certain elements (see  for details about the content restructuring) to their respective new locations. As long as these types of content do exist under /etc, AEM will work in a kind of "compatibility mode" and pick them up from /etc. Once you have moved everything out of /etc, AEM will start picking them up from their new locations.
With regards to your questions: while it is highly recommended to perform these steps during (or at least shortly after) your upgrade, it is not mandatory to do so. However, you will have duplicate and diverging content and not follow latest best practices.
In general, it is highly recommended to execute the common maintenance and clean up tasks before an upgrade/migration to reduce the amount of content that needs to be processed. First of all I recommend to manually go through your content and look for things that are no longer needed and might be cleaned up (= deleted). This is not an easy task and comes with quite some effort for "general" content, such as pages or assets. Other types of content might be easier to clean-up, e. g. deleting old packages (e. g. application deployment or content transfer) from package manager. After that initial step you want to check and execute the general maintenance tasks, such as revision cleanup, datastore garbage collection, version and workflow purge and the like (see ). There is also a dedicated documentation on pre-upgrade maintenance tasks that you should look at (see ). This documentation about revision cleanup has a dedicated section on upgrade considerations .