How does VMware vCenter Server work and what are the benefits over vsphere client

vCenter Server is basically a management tool that will allow you to manage VM's across multiple VMware hosts at once. You'll connect to vCenter Server with a vSphere client and instead of one host you'll see multiple hosts at once.

You can migrate VM's from one host to another via vMotion (although with Essentials you can't do it while the VM is running, and it requires shared storage). vCenter is especially useful for the more expensive VMware licenses, to manage things like DRS, HA, clustering and vMotion. With Essentials the use is more limited, but I also have Essentials and I've still found it to be quite useful to see my entire VM collection at once.

vCenter Server runs well in a virtual Windows box. It needs SQL Server Express or better and a 64-bit Windows OS.

VMware vCenter is an application that manages the ESX(i) nodes. You can use it do do clustering features, migrate machines from one host to another, etc. (read the whitepaper and documentation on VMware's site - too much to write here, and a lot of the features depend on the license you have).

Usually you want the vCenter on another PC, especially if you want to use the high-availability features. It uses a database (I think MSSQL Express by default), and some Java, end eats up a couple of gigs of RAM easily.

Of course, if you wish to manage each ESX(i) node by itself, and do not wish to manage another server, and have no need for advanced features, you can of course continue using just the vSphere client - with one VM per ESX, it might even be a lot easier :)

I'm not a windows admin, so I have no idea about the Exchange + vCenter combination.