Breathable polish is a nail lacquer formulated as a semi-permeable film with microscopic openings that let water vapour and oxygen pass through to the nail plate while the pigment and film stay in place.
Also known as: oxygen-permeable nail polish, halal nail polish, water-permeable polish, ademende nagellak
Ordinary lacquer forms a closed film. Breathable polish uses polymers borrowed from contact-lens chemistry, such as poly-HEMA, VP/VA copolymer and cellulose acetate butyrate with citrate plasticisers, to make a film with microscopic openings. Water molecules diffuse through while the colour stays put. Permeability is measured as a water vapour transmission rate under the ASTM D1653 test method (Halalworthy).
Inglot O2M made the first breathable claim in 2013. Orly Breathable, Nailberry L'Oxygéné and Tuesday in Love followed, and several are certified halal on ingredients and process (Refinery29).
The halal label and the wudu question are separate. Wudu, the ablution before prayer, requires water to reach the nail. Scholars are divided on whether water passing through a permeable film satisfies that requirement, and several rulings say it does not (IslamQA). A brand can call a polish halal-certified without it being wudu-friendly, and a buyer who needs the second should ask their own scholar.
For nail health the claim changes little. The nail plate receives its nutrients and oxygen from the nail bed beneath it, not from the air above, so ordinary polish does not suffocate the nail. Breaks from polish help for other reasons: fewer remover cycles, less staining and time for a damaged plate to grow out.