What does formal training in a field mean? I was curious what people mean when they say you need formal training in a field?
It means that this person has received explicit, recognized training, following the norms of the field. For instance, for a physicist this may mean having a university degree in Physics. For a medical practitioner this may mean having gone through med school. For a Linux sysadmin, it may mean having some recognized certifications.

The term is usually meant in contrast to learning through self-study or experience. For instance, we would say that a software developer has formal training if he has a degree in Computer Science, but not if he learned his trade solely by working through many online tutorials or through practical experience working in open source projects.