In 2012 Steve Chambers and Forrester Research coined the marketing term hyper-converged infrastructure (HCI) to describe a fully software-defined IT infrastructure that virtualizes all of the elements of conventional " hardware -defined" systems. HCI includes, at a minimum, virtualized computing (a hypervisor), a virtualised SAN (software-defined storage) and virtualized networking (software-defined networking). HCI typically runs on industry-standard commercial off-the-shelf (COTS) servers.
The primary difference between converged infrastructure (CI) and hyper-converged infrastructure is that in HCI, both the storage area network and the underlying storage abstractions are implemented virtually in software (at or via the hypervisor) rather than physically, in hardware. Because all of the software-defined elements are implemented within the context of the hypervisor, management of all resources can be federated across all instances of a hyper-converged infrastructure.
Hyperconvergence evolves away from discrete, hardware-defined systems that are connected and packaged together toward a purely software-defined environment where all functional elements run on commercial, off-the-shelf (COTS) servers, with the convergence of elements enabled by a hypervisor.   HCI infrastructures are made up of server systems equipped with direct-attached storage.   HCI includes the ability to plug and play into a data-center pool of like systems.   All physical data-center resources reside on a single administrative platform for both hardware and software layers.  Consolidation of all functional elements at the hypervisor level, together with federated management, eliminates traditional data-center inefficiencies and reduces the total cost of ownership (TCO) for data centers.    
The potential of the hyper-converged infrastructure is that companies will no longer need to rely  on different compute and storage systems, though it is still too early to prove that it can replace storage arrays in all market segments. It is likely to further simplify management and increase resource-utilization rates where it does apply.   
While hyperscale web services also use original design manufacturer x86 systems with software in custom ways, a model that is clearly scalable, they do so with a variety of optimized server types (some of which have no durable capacity) and storage approaches, not with one. See e.g. the variety of approaches in the Open Compute Project. Hyperconvergence is consistent in some key ways with this model, but it is simplified for smaller deployments by most vendors through focusing on one type of system and storage infrastructure, and this is believed to limit its success to date in mixed use, low latency and Tier 1 deployments at scale.