A private seller is one who is just selling off their own personal items such as clothes from their wardrobe, bits from their loft/garage etc. They wouldn't have multiples of brand new items to list (such as your vegetable chopper).
A Business seller is someone who buys or makes items to sell on. They need to be registered as a business to meet the requirements of UK law. They need to declare income to HMRC once they reach £1,000 worth of sales (eBay will be providing HMRC with your details anyway so it's vital to keep correct accounts for your tax return). You can obviously offset more expenses as a business seller, but can't offset any at all as a private one.
To correctly register as a business seller simply go to your Personal Information in your account and to the right of Account Type, which will be showing as 'Individual' you'll see an Edit option.
https://accountsettings.ebay.co.uk/profile
This doesn't affect your feedback profile or any current listings, it merely upgrades your account so that you're legally compliant.
If you're also selling your own items, just open another eBay account (you can have more than one).
