As if to my 14-year old;
On a PC you have the main chip - the one that runs Windows for you, but you also have others that do other things like talking to broadband or the hard-disk. Normally when Windows is off all of the other chips are off too. On a vPro PC, Intel have put a tiny little processer into one of those chips. It takes a tiny bit of electricity and it keeps just enough info, called the IP address, about the PC alive on the broadband (or ethernet) connection that another PC or a IT Administrator working on a central server can find it. If it can find it, it can wake it up and get Windows going. Or maybe your hard-disk is damaged or Windows wont start. Someone miles away, with the right tools can use that tiny little processor to send a small O/S like DOS (think of it like a small bit of Windows or Linux) and can work out whats really wrong with your PC and maybe even fix the problem without ever visiting you.
There are a couple of other things you can do too. Like, say you have a Virus Scanner on your PC. You can tell the vPro PC what its called, and if it ever dies the vPro PC can stop itself talking to any other PCs and potentially infecting them. Of course, in the same way you can start the PC up from miles away, you can shut it down too - which can save a lot of electricity if a company has thousands of them.
In fact, one of the simplest things you can do with a vPro PC that you can't do with normal PCs is to just count them - whether they are on or off. Again, that can be really useful to a company with hundreds or thousands of PCs and are trying to tell where they are. You can even record on the tiny processor what versions of what software is normally running on that PC and pick that data up when the PC is off. If some PCs have, say, the wrong version of Windows or their Virus Scanning software is old, you can wake them up at night and update them.
But hey, shouldn't you be studying ?