The default setting within an organization is to only allow Account Administrators to invite users. If you are an Account Administrator and you want to allow users, members specifically, within your account to add additional members and guests, it's effortless. Here are a few steps that will allow all members to add additional people to your account.
Note: once this is enabled, all members can add new users on behalf of you and your credit card will be charged for the new members and guests once their accounts are setup. However, only you are able to remove users within your account.
Within the sidebar, click the Settings icon.
Within the Settings dialog, on the left-navigation, click "Billing". Under the section, Administrator, click the slider next to the text, "All members can add additional people to the account". It should turn purple for on.
You're all done. Now members within your account will see the button, "New Member +" in Teams and Members, in addition to the button, "New Guest +" in Guests. See invite colleagues and guests for more information on how you and your members can add additional users.