libcurl provides three different ways to perform the transfer. Which way to use in your case is entirely up to you and what you need.
The 'easy' interface lets you do a single transfer in a synchronous fashion. libcurl does the entire transfer and return control back to your application when it is completed—successful or failed.
The 'multi' interface is for when you want to do more than one transfer at the same time, or you just want a non-blocking transfer.
The 'multi_socket' interface is a slight variation of the regular multi one, but is event-based and is really the suggested API to use if you intend to scale up the number of simultaneous transfers to hundreds or thousands or so.