Dear Ashish,
I use to get the same question when I started learning VMware. Let me make an attempt to convey my thoughts and let me know if they have helped you.
What is vSphere ?
vSphere is suite of products packaged shipped by VMware virtualization company, which includes products. Like VMware ESXi hypervisor, VMware vCenter Server, etc.
VMware ESXi ?
ESXi or hypervisor is bare metal OS which virtualizes x86 server hardware. You use ESXi ( OS ) installation media to install OS on top of hardware just like you install any other OS like Windows or Linux
Once you have VMware ESXi installed on a x86 server hardware I is ready to virtualized. What does it mean ? - It means you can now use same server to create , configure, run more than one virtual machines and install required Operating systems within Virtual Machines they are referred as Guest Operating systems which could be Windows or Linux etc
Further, vCenter server is another VMware Product shipped in vSphere bundle that helps you manage one or more ESXi servers from a centralized location.
I am hoping this answers your both queries.
Please let me know if that helps you and if you need any further clarification I will be glad to discuss with you further.
Virtually,
vAseem