Note: If you want to allow purchasing memberships / subscriptions online, also see Membership / Subscription Sign-up & Pay Online
If enabled, users can sign up and create their own account. These accounts will automatically be given a "request" (aka account or membership request) membership type defined in your Organization Settings as soon as they create their account. They will not be charged for this membership even if there is a price associated with it (you will be warned about this).
By default, the "request" membership type does not allow rental or check-out of items (though you can change this). This is to allow your organization to ensure the user, if they signed up themself online, fills out any required paperwork or agreements before you loan or rent items to them.
By default, admins can not check items out to users with a "request" membership as most organizations want to "approve" (check ID, confirm the account is real, etc.) before renting or loaning items to that user. You can either change their membership to a type that allow items to be checked out ("regular" by default) in the "Membership" Section of the Check In / Out page or by viewing their account and clicking on the "Membership" tab:
If you find there are large number of "request" users in the system, this may mean you have set your "Self Registration Membership Type" to be the same type as your "Default Membership Type" or another "approved" type.
To enable self registration, go to:
Settings -> Organization -> Edit Organization and make sure "Allow self registration" is checked off: