The only "Release" action you can do natively in JIRA can be found in your Project "Administration" Screen > "Versions" where you will see all the versions you have created for your JIRA Project (if you have one). If you hover the right most column, you will be presented with the cogwheel button for actions you can do and one of which is the "Release" action. This screen is available to anyone who have the "Administer Projects Permission" based on your permission scheme. Technically, no approvals are needed here. You just have to have the right permission to do so or someone who will need to give you that permission.
All of this is only assuming that you are talking about this feature. If you can give more context to your questions, we will provide more suitable answers
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