Some companies and organisations are exempted from having to pay VAT. Ror example, charitable organisations may get a certificate of exemption from the revenue commissioners. If you were to sell them, for example, a lawnmower (normally 21% VAT), you would invoice them at 0%.
You would, of course, ask to see their certificate of exemption, first,and take a photocopy for your records. If you had a VAT inspection, the inspector would expect you to be able to justify selling a mower at 0%.
Hope this helps.