Virtualization, generally speaking, has been one of those things that's easier to see and experience instead of explain. The concepts involved, while straightforward, can appear to be abstract to those used to non-virtualized environments. The easiest way that I've found so far to explain virtualization is that your computing hardware is now like an apartment building.
In a physical, or "bare metal" server environment, there are several components that mirror that of a house. There's the physical real estate of the house in the plot that it occupies. Servers occupy 1 or more U of rack space, or in some cases desk space. Houses have power feeds coming to them, as well as network (Internet). Servers have those same connections. Both have storage capacity, as well as other capacity metrics.
One of the simplest forms of multi-family dwellings is a large house that has been carved up into several apartments. Rather than let unused portions of the house to to waste, it was divided to allocate portions of space and utilities to each apartment. For all intents and purposes, each apartment is its own dwelling, containing its own space, power, and network, yet sharing a common piece of real estate and roof. The result is a higher population density and lower cost of living per occupant when compared to individual houses.
Modern servers are so powerful that most workloads don't need the full resources that a physical server can offer. In virtualization, a host is carved up into several smaller virtual machines. Storage, power, performance, and networking are split up so that each virtual machine has its own, as if it were its own separate server. Each virtual machine enjoys the resources it needs to function while saving the overhead, cost, and space of a full server.
In short, virtualization allows IT Pros to carve up server resources in order to lower cost and better utilize resources, much like one can turn a large house into apartments.