The service model in cloud computing that allows users to rent hardware resources is called Infrastructure as a Service (IaaS). IaaS provides users with access to virtualized computing resources over the internet, including servers, storage, and networking capabilities. This model allows businesses to scale their IT infrastructure according to demand without investing in physical hardware or maintenance. Users can provision, manage, and configure these resources through a web interface, resulting in greater flexibility, cost savings, and agility in their operations.