Hybrid license will allow you to run Exchange locally with out requiring a server license. Having an Office 365 SKU that includes Exchange online gives you the client access licensing (CAL) you need. Depending on how you are licensed and what you want to achieve will determine if the Hybrid license has any value for you.
The hybrid license is only valid as long as NO mailboxes are on the server. It's role is simply to manage object in a Hybrid environment. You can still use it as a mail relay for any on-perm applications that need to route mail.
If you do not have Software Assurance and want to keep the 2010 server, then the Hybrid License provide no additional value. You've already purchased a perpetual license.
If you have Software Assurance you should review your agreement as you no longer need to cover the Exchange server nor pay for Exchange CAL's.
If you don't have Software Assurance, but want to upgrade your server (since it will be around to manage Hybrid setup) then, here the Hybrid License can provide benefit as well.
To make use of the license just deploy the new Exchange server into your environment just like if you were preparing for an upgrade/migration. You'll license it with the Hybrid key and configure it like an on-prem server with all roles. Once it's configured correctly (interfaces moved, external access,etc) you can re-run the Hybrid Wizard and it will update your rules to include the new server. Be sure at this point to not select the 2010 server. Once this is finished you can go thru and decommission your 2010 server.