In meeting someone, there may be instant attraction on a chemical/physical and or psychic level "psychic" as in soul/mind, not supernatural). If not, over a short duration of becoming acquainted, a feeling of connection arises. This exposition will not address instant physical attraction, but references the emotional response brought about by energetic connection resulting from either conscious awareness, subconscious leanings, or both. The assumptions are not limiting nor encompassing of all forms of attraction to another.
The following categories of emotional attraction correspond to varied levels of personal evolution, differentiated along scales of emotional self-awareness, open-heartedness, and spiritual maturity.
1) The attraction comes from something that they have which is lacking in your own life, or something wanted. Perhaps it is lifestyle, attitude, or persona. This lack may or may not be conscious, and thus the drive behind the desire may or may not be realized. For instance, an introvert being attracted to an extrovert. A person who craves adventure in their life feeling attracted to a care-free spirit is also a good example. This type of attraction is the basis for the axiom "opposites attract".
2) The attraction originates from a sense of complement or balance. There is a sense that the person will bring balance in life and complement emotional desires or lifestyle choices. This calls for being a step up the hierarchy of self-awareness -- in some cases. Athletes dating other athletes is a good example: there are complementary activities and habits to share. Being attracted to someone with a similar lifestyle and outlook falls into this category: the person demonstrates similarities, rather than the differences found in the "opposites attract" phenomenon, as mentioned above. Those on a specific life path seek others on the same path, for example. On this level, the attraction tends to stem from conscious awareness, emotional maturity, and relational experience. Then again, this "like attracts like" theory may be due to social and cultural mores, and thus, the attraction is birthed from hidden motives forced by unacknowledged external pressure.
3) The attraction originates from the recognition of Yourself in the Other. Not only is there coincidence in outlook and lifestyle, and perhaps even a balance of some opposite (yin-yang), but there is recognition of the true Essence of the other, regardless of differences. There is no unconscious search to fill the lack. There is no unconscious search for an opposite. There is resonance in lifestyle and acknowledged common desires. Balance in life is near or has already been attained, and the only search is the one for a companion with whom you can share the evenness of life. In recognition of the fullness and completeness of one's own Self, in acknowledging connection to all life, in knowing the human need for connection, the other is seen as part of Self and part of that greater Whole. Divine nature is recognized and they are held in love, with space for freedom to remain or to leave. Since one embodies fulfillment and completion, there is no need to seek it in another. This third type of attraction encompasses emotional awareness, authentic relating, open-heartedness, compassion, and spiritual maturity.