First, let me distinguish between soul-mates and twin-flames, for they are actually two very different complements...
By my own understanding, we each have many "Soul-Mates", those kindred souls upon Earth with us, from our own higher-dimensional soul-family. Soul-mates usually have agreements with each other prior to coming into this life as to what role each will play in the "theatre" of life. Soul-mates are usually of complementary vibrations, and work together as a sort of soul "family", assisting each other in Spiritual growth and discovery of Self... Soul-mates can be brothers, sisters, friends, co-workers, or in intimate partnerships with each other, but share a close bond and understanding on many different levels and lifetimes. However, soul-mates are usually two different Higher Selves, different souls that are part of the same "family" or frequency in a spiritual sense.
Twin-Souls are another matter entirely... They are actually two polarities of the same original soul-essence. They maintain different personalities and natures, yet each complements the other, almost like two puzzle pieces fitting together where they are very different, forming another completely unique essence. Each twin-flame must be very strong in their own self and spiritual awareness before it is possible for them to unite totally on the Earth plane, for only then is it possible to ascend and reunite all levels of being on all planes of existance. In this process, their two selves will remain distinctly unique, like two seperate circles of personality, yet there is a center "melding" point where the male and female unite as the circles overlap in the center, forming a third, the sacred trinity...
According to the book, "Twin-Souls", by Joudry and Pressman:
"At the summit, (of ascension) is perfected love, every created soul loving every other. The foundation is the love of men and women. Whenever people meet in love exchange, there is an ascension of their souls. When Twin-souls reunite, the ascendance is jet-propelled. The twin-souls join the God force that draws all life upward.
They are more than the sum of two; they are three..."
"Close as they will be when they find each other upon Earth, the one soul will still still inhabit two individual bodies, (and personalities/egos). They will grow in oneness increasingly as they scale the heights of spiritual existance in the afterworld. Yet they forever retain their indivual natures within the unified soul.
Bulgarian Master Omraam Mikhael Aivanhov also has a beautiful description of Twin-souls:
"Every human being has a twin-soul. When man leapt like a spark from the bosom of his Creator he was two-in-one, and these two parts complemented each other perfectly, each was the others twin.These two halves became seperated, they took different directions, and they have evolved seperately. If they come to recognize each other at any point in their evolution, it is because each carries the image of the other in the depth of his being, each has put his seal upon the other. Thus, each carries the image of his twin-soul within. The image may be blurred but it is there. For this reason, everyone who comes to Earth has a vague hope that he will find a soul who will be everything he needs, and that with this soul he will find indescribable harmony and perfect fusion.
Twin-souls complete each other; no other person in the world can so complete them.
Thus, all beings you have met since the beginning of your multiple incarnations, all the husbands and wives you've had, all the lovers or mistresses, have all left you, because they were not for you.
Perhaps you were together for a while, like a pot with a lid that doesn't match. Wheras two Souls whom God has created together are absolutely made one for the other, and nothing can seperate them, truly, they have no fear of being seperated.
In a married couple, when one or the other is AFRAID that someone may 'rob' him of his partner, (and nothing can keep this from happening), it is because that partner is not truly the beloved, not the TRUE beloved, the twin-soul...Twin souls recognize each other with absolute certainty and can never truly leave one another."
The twin-soul may actually be very near, either someone you have known all your life, or else just on the edge of your perception, awaiting the last steps you both need to take in growing in order to reunite. The true union can only take place AFTER the point of reunion has occured within ourselves, and our Male and Female energies are balanced within...
For signs you are ready to enter a twin-flame relationship or merging, see: Are you ready for a Twin-Flame relationship?