Well, I'm not going to go into the whole detail of everything but I can outline the basic differences here. You can see the packages themselves on the main eUK site.
The main difference between your current shared hosting platinum package and a reseller package is everything is more compartmentalised. In your current package, you'll have one login for cPanel for which you create addon domains for all your sites etc. In a reseller, you'll get a reseller login for cPanel and another control panel called WHM. You are able to create individual accounts in cPanel for your clients e.g. businessdomain.com and artistdomain.com are two completely separate people who you provide
web hosting for and you can create accounts so one is not aware of the others presence and they will have complete control over their own cPanel setting, including email accounts etc. Further more, as the reseller, you can access all the accounts you have created/are under your control using your cPanel login.
WHM allows you to create these accounts (with certain bandwidth and space limitations etc.), configure the DNS and other such things. It's a while since I've been on a reseller and there are more restrictions compared to WHM on a
VPS Hosting (i.e. they don't want you to be able to reboot the server and things like that) but it's basically more of an admin panel.
So to summarise, you'd be able to completely separate your accounts from each other so you can tell exactly what each client is doing and then each client can have full control of their hosting account. It takes things out of your hands and lets them do things without having to go through you. But you still have access for when you need to.