Giftedness is SO misunderstood.
I really cannot over-emphasize this.
People in Western culture tend to equate giftedness with exceptional achievement and performance. Put differently, according to Western society, only individuals who can demonstrate outstanding ability (often in more than one area or domain) are deemed gifted (Silverman, 2013).
Giftedness is much more than outward performance and achievement, however (though it surely can include both).
In fact, many gifted individuals do not at all appear gifted. For example, gifted persons from several groups—women, people of colour, non-English speakers, and those of lower socioeconomic status—are often not able to develop or display their gifts due to widespread societal stigma. Moreover, it is common for gifted individuals to struggle inwardly with self-doubt and low self-esteem due to feeling out-of-sync with others. Combined, these external and internal factors stunt many gifted peoples’ growth, leaving their many potentials unrealized (Silverman, 2013).

So, if giftedness is not (just) exceptional achievement and performance, then what is it?
Fundamentally, giftedness is a unique way of being, knowing, and doing. Giftedness is a different way of perceiving and experiencing life:
vivid, absorbing, penetrating, encompassing, complex, commanding – a way of being quiveringly alive (Piechowski, 1992, p. 181).
Renowned expert Annamarie Roeper (1982) describes giftedness beautifully. She states that it is,
a greater awareness, a greater sensitivity, and a greater ability to understand and transform perceptions into intellectual and emotional experiences (p. 21).
While this enhanced awareness and sensitivity can lead to exceptional achievement and prodigious productivity, due to the inner and outer factors discussed previously, the movement from inner gifted experience to outer gifted accomplishment is surely not guaranteed.
Perhaps you are wondering: might I be gifted? (and, like most of us gifted folk, probably concurrently doubting that you ever could be!).
I hope my characteristics of the gifted page can clarify things for you.
References:
Piechowski, M. M. (1992). Giftedness for all seasons: Inner peace in time of war. In N. Colangelo, S. G. Assouline, & D. L. Ambroson (Eds.) Talent Development. Proceedings of the Henry B. and Jocelyn Wallace National Research Symposium on Talent Development. Unionville, NY: Trillium Press.
Roeper, A. (1982). How the gifted cope with their emotions. Roeper Review, 5(2), 21–24. http://doi.org/10.1080/02783198209552672
Silverman, L. K. (2013). Giftedness 101. New York, NY: Springer Publishing Company.