From the 13th century an apprentice was a young male who was undergoing training in a trade and had not yet completed his training. As a result he would not as yet have been acccepted into a guild as a journeyman.
Typically an apprentice would live in the home of his master for between 2 to 7 years and would have secured the position by his parents paying the master to take him on. He was usually not allowed to marry.
Note that usage of terms like "apprentice," "journeyman," and "master" (and, indeed, "guild") varied widely depending on time and location.
Apprentices in the SCA
Within the SCA this person has a 'relationship' with a Laurel - who takes on the training or wellbeing of the Apprentice, and will promote and help them with their activities and crafts. An apprenticeship does not convey any official rank.
The nature of this relationship varies from Laurel to Laurel. Some Laurels require their apprentice to swear fealty. The duration of the apprenticeship may be agreed upon beforehand by both parties, and could be until the apprentice becomes a Laurel, for a fixed time period or until the apprentice has advanced sufficiently to become a journeyman. Most apprentices wear some sort of token to indicate their status, often a green belt with the Laurel's device on it. (Note that the practice of color-coding your dependents varies a lot from place to place.)
See Also: Lochac Laurels Guide to Apprentices
Apprenticeship can also be a level in a Guild. Some guilds replace "novice" with "apprentice."