Master Numbers in numerology.

The first part of this text is an excerpt from the book Numerology; Key To Your Inner Self.

There are 3 double-digit numbers that, while they are rooted in the single-digit numbers, require special emphasis and attention. These are 11, 22, and 33.

They are called Master numbers because they possess more potential than other numbers. They are highly charged, difficult to handle, and require time, maturity, and great effort to integrate into one's personality.

The 11 is the most intuitive of all numbers. It represents illumination; a channel to the subconscious; insight without rational thought; and sensitivity, nervous energy, shyness, and impracticality. It is a dreamer. The 11 has all the aspects of the 2, enhanced and charged with charisma, leadership, and inspiration. It is a number with inborn duality, which creates dynamism, inner conflict, and other catalyses with its mere presence. It is a number that, when not focused on some goal beyond itself, can be turned inward to create fears and phobias. The 11 walks the edge between greatness and self-destruction. Its potential for growth, stability, and personal power lies in its acceptance of intuitive understanding, and of spiritual truths. For the 11, such peace is not found so much in logic, but in faith. It is the psychic's number.

The 22 is the most powerful of all numbers. It is often called the Master Builder. The 22 can turn the most ambitious of dreams into reality. It is potentially the most successful of all numbers. It has many of the inspirational insights of the 11, combined with the practicality and methodical nature of the 4. It is unlimited, yet disciplined. It sees the archetype, and brings it down to earth in some material form. It has big ideas, great plans, idealism, leadership, and enormous self-confidence. If not practical, the 22s waste their potential. Like the 11, the 22 can easily shrink from its own ambition, causing difficult interior pressures. Both the 11 and the 22 experience the pressure-cooker effect very strongly, particularly at an early age. It must work toward the realization of goals that are larger than personal ambition. The 22 serves the world in a practical way.

The 33 is the most influential of all numbers. It is the Master Teacher. The 33 combines the 11 and the 22 and brings their potential to another level. When expressed to the fullest, the 33 lacks all personal ambition, and instead focuses its considerable abilities toward the spiritual uplifting of mankind. What makes the 33 especially impressive, is the high level of sincere devotion. This is shown in its determination to seek understanding and wisdom before preaching to others. The 33 in full force is extremely rare. 

The number 33 only matters when found among the core numbers: The Life Path, Heart's Desire, Expression, Personality, Maturity number, or as an Essence cycle or Pinnacle cycle. In all other cases the 33 should be reduced to a 6.
The fact that the 33 is extra-ordinary demanding and rare can be seen symbolically in the methods of calculation. 
For example, a 33 Life Path can happen only when each of the 3 units of the birth date (month/year/day) add to 11. Or when the year adds to 22 (in the 20th century there are only 7 years that add to 22: 1939, 48, 57, 66, 75, 84, and 93) and the month and day of birth combined total is 11. And finally, when the birth day is 22 and the month and year of birth total 11. 

Another way to look at the Master numbers:
The Master numbers 11, 22, and 33 represent a triangle. A triangle of Enlightenment.

33

11             22

The number 11 represents the vision.

The number 22 combines vision with action

The number 33 offers guidance  to the world.