One core can do plenty of things at a time (using a kind of time-sharing), but the more cores you have the more they can all handle IF the software is written in a certain way which I believe a lot is these days – especially if it's serious software that knows it takes a lot of power ie Photoshop filters and so on.
If you want to run one intensive aplication at the same time as another, then multiple cores help – ie encoding video AND doing other stuff at the same time.
It's worth noting though that your PC likely only has one disk, so only one application can read off the disk at once and most apps are reading from disk a lot.. you can mitigate this if you have two disk for example if you want to encode video, you put the video files all on one disk and then windows and everything else on another – that way your encoding process will run on one core and have a disk all to itself and your other core(s) can do whatever they want with their own disk.
It's also worth noting that the vast majority of software hardly uses the CPU at all – if you are sending email or writing a doc, your CPU does practically nothing. So having Outlook say on one and word on another will make no difference to if you were using them on the same core. Only stuff like video, image processing, games etc use full CPU power.
If the software reocmmends it, then they have probably designed their software to take advantage of multiple cores, so go for it. Also get tons of memory because as noted above, if you really are gonna use 4 cores then you'll also benefit from lots of RAM.