Asexuals (sometimes abbreviated to asexes) are people who don't tend to have much sex, by choice.
Most asexuals consider themselves to have reduced or negligible sex drive. Someone with a normal sex drive who chooses not to have sex would more accurately be described as celibate, but naturally there is overlap.
Many asexuals feel romantic attraction; some enjoy cuddling and other physical expressions, but some do not. Some are happy to cultivate a circle of close friends in place of a desire to pair off. Some form, or seek to form, exclusive platonic partnerships. Some form arrangements with two (or more) partners, in order to take pressure off the asexual to have sex.
Asexuals are neither shockingly unusual nor startlingly original. Amoebae thought of this first, and collectively have a lot more un-experience.
While most characters are not interested in being sorted on the basis of sexual orientation, here are some examples: