A field is an area of study or work; If something is your field, you know quite a bit about it and could be considered an expert in it.
I want to major in English, creative writing, or something in the field of literature, but my parents do not think there will be many job opportunities for someone with a humanities degree.
When I started work in the field of computer science, the Internet was a new idea that few people understood. Today, all my clients use web based software in their offices and need to access the Internet every day.
If you are out in left field, you are not where you need to be. You either don't understand something, or you are unaware of something that you need to be aware of. This expression comes from baseball and references the long distance between the person covering left field from first base. If your ideas or you are out in left field, you are far off from the norm or from where you need to be.
I don't know how I missed the deadline for my research paper, but I felt as if I were out in left field when the rest of the class began to turn their papers in at the beginning of class today.