Three is an important figure in numerology, for it denotes that which is completed, or that which has reached the end of an appointed phase.
Of course, when one phase ends we must, of necessity, begin another. This is the case with 3 - having completed one particular stage in life there is always movement or progress. This forward momentum is usually built upon whatever has been attained in the early work of the individual.
So 3 might be seen as a logical progression from the 1, where we saw the ego - the primal force; and the 2 where we saw that force beginning to integrate and work in harmony with others. The 3, therefore, might be considered to be the end result of this initial integration of forces.
There are lots of symbolic connections with the number - the Father, Son and Holy Ghost trinity of Christianity, the same principle echoed in the Isis, Osiris, Horus mystery of Egyptian tradition; the three faces of the Goddess as virgin, mother and hag in pagan mythology. You can probably see from each of these that we see two independent units which merge to produce the third element of the trilogy.
You might also compare this effect in relationships - two independent people coming together, and between them create the third principle of the relationship. It is a creation which has come about as a result of the actions and energies of the two people involved. It is wholly unique, and neither of the initiating partners would be able to create the same relationship with anyone else.
In numerology, 3 is much concerned with one's ability to enjoy life. People who have this number featuring strong in a numerological analysis are considered to be outgoing, convivial and gregarious. This effect of going outward and sharing experience with others is a continuation of the general theme of the number, in that, it acknowledges the concept that when 1 merges with 2, 3 results.
3 is also much concerned with matters of intellect and growth - you might be able to understand that in order to complete one phase (that is of being differentiated) and to join with someone or something else to create a new 'thing' we must fall back on our ability to communicate, our intellectual understanding of reactions which have their roots outside of us.
We need to think about other people's reactions and responses, consider their needs and feelings, concentrate on the growing entity which we are both creating. Therefore, we are thrown back onto our intellectual reactions. We need to think through what happens - how it affects us, which direction it appears to take - and we also need to be able to share that with the person on the receiving end. This means that we are consciously assimilating what happens to us. Three is associated with yellow, and that color is responsible for stimulating the mentality and intellect. Most of our reasoning processes take place under the influence of the color yellow. It activates our ability to think logically.
You can see, then, that 3 is a number much linked with our ability to merge, share and join with others. Perhaps you can also see that 3s emanate from the combined force of the Ace and the 2.