Positions are the individual roles a person in a team takes on in battle.
The Definition of the Position
The battles in the Tower are mostly fought as teams and the Position (포지션, pojisheon) of an individual is the role they play in a team. Of course it's possible to battle without dividing into specific Positions, but it's more efficient to utilize Positions. Most of the names of the roles are derived from the battles of the first 10 Great Families, as such, they are mainly based on the men vs Shinheuh battles, rather than the men vs men battles. However, this doesn't mean that current Positions are worthless in men vs men battles.
As the importance of the men vs men battles in the Tower increase more than ever, current Positions are evolving accordingly. All Positions have to make a contract with a Guardian so they are able to use Shinsu for purposes like Shinsu strengthening.
Note that one person is not limited to one position. Prince is a Light Bearer, yet possesses Fisherman equipment, and Khun Ran is a Fisherman, but can take the Spear Bearer position with his Lightning Spear techniques. Scouts like Hatsu would also be good at the Fisherman position and Scouts like Leesoo would be good at commanding and strategizing, hence his suitability for the Light Bearer position. Apple is capable of being both a Scout and Light Bearer. Rankers on the level of a High Ranker, like Yu Han Sung, is regarded to be capable of handling all the Positions, while the top rankers such as Urek Mazino Zahard and the 10 Family Heads are all capable of taking up any and all positions masterfully.
Although there is also a position named Fisherman, the term "Fisherman" (낚시꾼을, nakksikkun-eul), when used in a general sense is used to refer to someone that is a perfect combatant capable of fighting in all types of battles; "Fishermen" (낚시꾼은, nakksikkun-eun) is the plural term.
- Fisherman (낚시꾼, nakksikkun; "Angler")
The main offence of the battle, Fishermen are to dash into the heart of the enemy force and decimate their forces, usually through physical attacks.
- Spear Bearer (창지기, 搶지기; "changjigi" or "Spear Keeper")
Spear Bearers act like snipers for the team, throwing their spears with deadly accuracy, but they can also serve a purpose similar to the Fisherman's by using their spear like a staff for close-combat. Technically speaking, they take all long-range matters into their own hands.
- Scout (탐색꾼, 探索꾼; "tamsaegkkun" or "Observer")
Scouts are tasked with reconnaissance, which usually involves running ahead and investigating enemy forces for information, then returning and delivering the intel to the Light Bearers. Additionally, they can help the Fishermen with offense if necessary.
- Light Bearer (등대지기, 燈臺; "deungdaejigi" or "Lighthouse Keeper")
Light Bearers are responsible for gathering, storing and delivering crucial knowledge to their team-mates while guiding them with the light of their Lighthouse. Light Bearers are usually the most support-oriented position.
- Wave Controller (파도잡이, 波濤잡이; "padojabi" or "Waver")
Wave Controllers are the directors of the battle, aiding their comrades by healing their wounds, annihilating enemy forces or subtly changing the tide of the battle, all through the use of Shinsu. There are many variations of this Position.
A special position (특수 포지션, teuksoo pojisheon) refer to additional roles one can carry besides their primary battle position, so special positions can be overlapped with another position, there is no case in which one only holds a special position without any primary battle position. In some cases one may have several special positions, and in other cases, one may have none, all depending on the person. 
- Guide (길잡이, giljab'i; "Pathfinder" or "Assistant")
The Guide is considered a Special Position, but it plays no specific role in combat. Guides lead the way for the team, usually with their ability to see into the future and excellent analysis skills. It is a very rare Position and they are considered "blessed" by The Tower.
- Defender (디펜더, dipendeo)
Defender's main aim is to protect the Light Bearer and/or Spear Bearer.
- Anima (부리미, burimi; "Subjugator")
An Anima controls living beings, commonly Shinheuh. It seems it's more a talent than a technique, as one cannot just become an Anima through learning.
- Wonsulsa (원술사, 圓術師; "Circle-technique user" or "Circler")
- Dansulsa (斷술사, 단術師; "Pressure-technique user"? or "Pressurer"?)
Dansul is the ability to, from far away, create an area with an enormously large amount of Shinsu pressure. Dansulsa may be a sub-category of Wave Controllers.
- Hwayeomsa (화염사, 火炎師; "Flame user" or "Flamer")
A flame user is a person able to form flames from Shinsu currents.
- Jeonsulsa (전술사, 電術師; "Lightning User" or "Lightninger")
A Lightning user is a person able to form electricity from Shinsu currents.
Notes and Trivia
- In a SIU blog post, he hints that as the story develops beyond the 20th floor, battles that utilize positions, such as combinations like Light Bearer-Spear Bearer and Scout-Fisherman will become more frequent.
- If positions fight each other, the Fisherman will usually win.
- SIU FanCafe Question And Answer (By Bunnyasbanana)
- User blog:GoDai/GoDai's Translations: People and Groups (3) - All about Positions#Subjugator
- Vol.2 Ch.154: 36F - Hell Train: Hoaqin (2)
- Siu Blog
- GoDai Blog
- Ch.28: 2F - Position Test (1); Lero-Ro's explanation.
- Vol.2 Ch.30: 21F - Flower of Zygaena (2); blog post
- Translation of Q&A