If you're a trainee, you're being taught to do a new job. If you're hired at your local grocery store, you'll likely spend some time as a trainee before you're allowed to work the cash register on your own.
Whenever someone goes through training, especially for a new job or skill, they can be called a trainee. If you're learning a new computer coding language, you might be a Python or Java trainee. And if you're in your first week at a coffee shop job, you're probably still a barista trainee. Trainee dates back to the mid-19th century, from the verb train, "instruct."