VMware vSphere is made up of two products: VMware ESXi and VMware vCenter. When both of these are installed and running to support the virtual machine architecture it is called vSphere. 

VMware ESXi is an enterprise type-1 hypervisor that is installed directly  on a  server.  VMware ESXi allows you the ability to run virtual machines. Even though you run ESXi directly on a server only minimal configuration can be performed locally (using keyboard/monitor).  Most of the configuration  and configuration of VMs will be done using a web based user interface. Earlier versions of ESXi actually required you to have a client installed on your computer to connect to manage and configure VMs. 

VMware is an industry leader in Virtual Machine and Container technology, so it is important to also familiarize yourself with how VMware does things. 

A datastore is used by ESXi to store virtual disks.  A datastore uses VMFS (Virtual Machine FIle System)  as its filesystem. This filesystem is optimized for storing VMs and also hides the specifics of the physical storage from VMs.  

Once you have VMware ESXi installed and running on a server you will then want to create a vSphere virtual machine. vSphere is a tool that you will use to help easily manage your data center or ESXi hosts. When you use vSphere you can easily manage up to 1,000 ESXi hosts and around 10,000 virtual machines! Just imaging try to manage all thoses ESXi hosts and VMs through multiple web interfaces. You'd go nuts!  vSphere also helps to provide security due to the ability to assign roles to users. If you are not going to run VMware vSphere you will be limited on what you can do as Sphere is required to do some more advanced features.