Vomit contains stomach acid and has a pH level of about 2, the same as pure lemon juice. However, sometimes it is a lot lower. The main constituent of vomit is stomach acid (hydrochloric acid) which is a very strong acid, often pH 1. Saliva and your mouth on the other hand have a pH of about 6 or 7. If that pH level drops below 5.5 (which will happen if you expose your mouth to vomit), your teeth start to dissolve (only a little at a time, but it adds up over time).
In addition, this acidic pH level will irritate your piercings, making them take longer to heal and potentially causing them to flare up even after they are healed. Food matter can become stuck in your piercings, so if you vomit, immediately rinse well with water (but try not to brush for about an hour to avoid damaging your teeth). If you have an eating disorder that causes you to vomit regularly, you may want to consider addressing it prior to getting oral piercings.