Jains cover the mouth (muhapatti) mainly to follow non-violence (ahimsa). By keeping a cloth in front of the mouth, they aim to prevent inhaling or accidentally harming tiny airborne beings and microorganisms, and they also keep their speech mindful and controlled.

• In Śvetāmbara traditions, many mendicants wear muhapatti regularly, and lay devotees often use it in temples or during prayer.
• In Digambara traditions, the practice is used differently by various sub-groups, with some using it less prominently or in specific situations.

Overall, the mouth-cloth is a visible sign of a Jain commitment to ahimsa and careful speech, as well as a practical measure to minimize harm to micro-life around us.

You can read more here and here