An apprentice is someone who learns a trade. An apprentice farmer is paid very little but has the chance to learn farming by watching and doing.
In the old days, becoming an apprentice was the only way to get into many lines of work. Nowadays we think of it more in terms of trades — butchers, bakers, bricklayers, etc. If you do the same thing in an office setting, it's usually called an internship, but the idea is the same — learning by watching an expert. The word can be used as either a noun or verb: You are an apprentice, but you also can apprentice to the barber down the street.