organically grown vegetables; pesticide-free vegetables
Refers to vegetables grown without synthetic pesticides. In Japan, this term is often used in marketing and everyday conversation, though the official organic certification (有機JAS) uses different terminology.
This supermarket carries pesticide-free vegetables.
Pesticide-free vegetables are a bit more expensive, but you can eat them with peace of mind.
有機野菜 is the official term for certified organic vegetables under the JAS system, while 無農薬野菜 simply means no pesticides were used and may not imply full organic certification.
Compound of 無 (mu, 'without'), 農薬 (nōyaku, 'agricultural chemicals/pesticides'), and 野菜 (yasai, 'vegetables').