3d6 In Order

Playing What Is Rolled
In Volume I: Men & Magic the referee is instructed to roll three six-sided dice in order to determine each character's abilities.  The player then selects a character class using those scores as a basis for the new character. Three six-sided dice in order for Strength, Intelligence, Wisdom, Constitution, Dexterity and Charisma. High scores, 13-18, in the chosen class's prime requisite adds to experience earned and helps the character advance through levels more rapidly. A low score, 8 or less, deducts from earned experience and slows advancement. This seems to be the most important contribution of ability scores in White Box.
There is no Strength bonus for attacks and damage in White Box. There is no improvement to Armor Class for high Dexterity. Dexterity scores do affect missile "to hit" chances slightly with a +1 for Dexterity scores above 12 and a -1 penalty for Dexterity scores below 9. Constitution scores affect survival chances and can add 1 to each "hit die" if the score is at least 15, or even subtract 1 from each "hit die" if the Constitution score is 6 or less. Charisma is perhaps the most useful ability score after the prime requisite as it affects how the player character interacts with people and monsters in the milieu. A high Charisma score allows the character to attract more hirelings and increases their loyalty base. A high Charisma may also be useful in persuading a captor to keep the character as a valued prisoner rather than kill them, enslave them or turn them into swine.
I can only speculate as to why White Box suggests the referee roll the dice determining each new character's ability scores. It seems likely this is done to give the referee some control over what scores make for an acceptable character. I presume that scores which seem to suggest a hopeless character can be rejected by the referee before the character is handed over to the player. Once the player takes control of the new character the player determines race, class and alignment and rolls 3d6 x 10 for starting gold pieces and a single d6 for "hit points". It is therefore the ability scores that White Box places in control of the referee.
The rules state that Clerics can use Strength on a 3 for 1 basis in their prime requisite area (Wisdom) for purposes of gaining experience only. Fighters and Clerics may use Intelligence on a 2 for 1 basis  in a similar manner. Fighters may use Wisdom on a 2 for 1 basis and Magic Users on a 3 for 1 basis in their respective prime requisite areas. Changing character class (not recommended, but apparently allowed) requires a score of 16 or better in the prime requisite of the new class and the score must be unmodified (i.e. not adjusted in the above manner). White Box is a bit unclear as to whether the use of Strength, Intelligence and Wisdom to enhance the prime requisite is an actual lowering and raising of the scores or just a way to figure the prime requisite experience bonus without actually changing the scores. I rather favor the latter interpretation of the language "for purposes of gaining experience only".
Dr. Holmes transfers the responsibility for rolling the three six-sided dice generating scores for each ability to the player as the first step in creating a character for his 1977 edition of the Basic game, but also makes the provision to set aside a "hopeless" character. Dr. Holmes uses the same prime requisite, Constitution and Dexterity score bonuses as those listed in White Box Volume I except that Dexterity is the prime requisite for the new Thief class.
The early game editions make little use of the ability scores beyond the prime requisite experience bonus. Ability scores seem to mostly assist the player in determining which class to choose for the character and perhaps help shape the character concept in terms of what manner of strengths and weaknesses the characters possess. An emphasis on playing what the dice rolls give you is an essential element in play.
Playing the character rolled becomes more difficult as ability scores take on additional meaning as in later editions. It is not uncommon for house rulings in White Box to incorporate rolling against an ability score to determine the occasional outcome of an action. However, low scores in abilities rarely significantly impact the character except perhaps in the case of the prime requisite. Once high ability scores start to carry significant advantages such as the Strength bonuses given in Supplement I: Greyhawk, those scores can directly influence character power level and high rolls become greatly desired. The Dungeon Masters Guide published in 1979 for the Advanced Game suggests multiple methods of increasing the odds of higher ability scores by rolling more dice, dropping the lowest scores or choosing the best set of scores from as many as a dozen ability roll sets. The original random distribution is thus skewed  dramatically toward the high end. More recently a point-buy system whereby scores are assigned to each ability and balance between characters sought in assigning higher costs to the higher scores with limited resource points thus allowing the player to tailor their PC to a preconceived ideal.
In White Box character generation is meant to have a significant random element. It is meant to be quick and get the player ready to play in a minimum amount of time. Chargen can be done at the table while the game is proceeding if a character "dies" during an adventure session. The campaign itself is not tied to any single character and the milieu plays a more central part in the continuity of play than does any PC. Character personality is developed during play, or is created from the imagination of the player who may decide to record an elaborate backstory and personality profile as part of their character data.
In play what really matters is the fun everyone has at the table. The stories that are told afterwards are hopefully about what so-and-so did, what new and exciting discoveries were made, what unexpected surprises were uncovered, and what unexplained mysteries remain. When discussing our hobby with other players, I would much rather hear about adventures than characters. It is part of my old school approach to gaming that I am much more interested in milieu and adventure than clever character builds.
Play what you roll, PC's are not special snowflakes, and don't tell me about your PC, rather tell me about your adventures. Those are the rules at my table.