The file you are trying to upload is a SharePoint solution package. You can upload it (presuming it's not a sandboxed solution) via stsadm or the management console on one of your web front-ends. After deploying the solution package, a site collection scoped feature will be present that you can activate to make the webpart available in your site collection.
If it's a sandboxed solution, you can upload it via site actions (in the root site of your site collection), site settings, solutions (under galleries). In this case, you don't need access to the web front-end.
Best Answer
You can manage webparts from:
and click "Retract Solution".