The three wires in a mains supply are at different potentials. The live wire is at a potential difference of about 230 V compared with earth. The neutral wire is at about 0 V, and the earth wire is at 0 V.
This means the p.d. between the live and neutral wires is about 230 V, and the p.d. between the live and earth wires is about 230 V. The p.d. between the neutral and earth wires is about 0 V.
This is why the live wire is the dangerous one. A person standing on the ground who touches a live wire has a p.d. of about 230 V across them, and a current can flow through their body.