Not to be confused with being genderless, nor with biological asexuality (which refers to organisms that do not reproduce sexually), asexuality, in the most basic sense of the term, is defined as a sexual orientation where a person doesn't experience sexual attraction towards anyone.
It's similar to how a heterosexual person does not experience sexual attraction to their own gender, but applied to everyone.
But the concept of asexuality is not quite as black and white as it may seem at first. Asexuality is also an umbrella term for people that fall between asexuality and other orientations.
RomanticismRomanticism and sexuality are two distinct—if parallel—spectrums. Some people use the split attraction model for themselves, with labels such as homoromantic asexual being used. However it should be noted that homo/hetero/bisexual/etc labels do not refer solely to sexual attraction; etymologically, the "sex" part referred to gender, which it was considered synonymous with. Labelling homosexuality as being inherently sexual comes loaded with baggage, so please don't.
Asexuals don't feel sexual attraction, but not all asexuals are aromantic. For a Romantic Asexual, romance isn't a problem, and many are comfortable with cuddling and kissing to express their feelings—they may be part of a Chastity Couple. Meanwhile, there are also aromantic sexual people, who may be part of a Friends with Benefits arrangement. Even an aromantic asexual can still have other types of relationships, like Platonic Life-Partners, that fill a similar role in their lives.
SexSome asexuals are repulsed by the idea of sex. Others don't mind it. Sex doesn't have to be disgusting, it's just not something that they feel has any place in their lives.
Some asexuals do have sex with their life partners, to make them happy—similar to going to a movie with your girlfriend, because you like making her happy, even though the movie doesn't really interest you. Others may choose to have sex because they want children. They may even enjoy it when they actually "get around to it", although it probably takes a while to "warm up". But it's just not something they find all that fulfilling. A popular analogy is to use food; "I'm not hungry, but I can still eat for pleasure."
Some asexuals do actually masturbate and enjoy doing so, as physiological arousal is considered to be distinct from sexual attraction, and these people can still be either neutral or repulsed by the idea of having sex with another person regardless. For them, the libido is an undirected physical urge, like sneezing, using the bathroom, or scratching an itch.
Many asexuals consider asexuality to be a spectrum between "fully" asexual (never feel sexual attraction) and "fully" allosexualnote . Various terms exist to define people who are not fully asexual but fall within the spectrum:
Gray asexuality is an umbrella term that describes the 'gray area' between sexuality and asexuality and covers a various range of identities under the asexual spectrum. In general, they do not feel sexual attraction except under certain circumstances and/or toward certain individuals. They could simply be attracted to an unusual characteristic (physical or behavioral), or only want to engage in a very specific type of sex. Gray aces are considered part of the asexual spectrum despite their ability to feel sexual attraction because it happens so rarely that in most situations, they may as well be "fully" asexual.
Demisexuality is a subset of gray asexuality, and specifically refers to people who only experience sexual attraction after a close emotional bond has formed, although the definition of 'emotional bond' varies from person to person. It does not refer to people who are picky about their sexual partners, or people who are "saving themselves for the right person": these people may experience sexual attraction, but choose not to act on it, while demisexuals don't feel ANY sexual attraction at all without a preexisting bond.
Many people who describe themselves this way, or could be described this way, have had multiple partners in their lives (some are even polyamorous). Asexuality is not a 100% accurate description for them, but understanding the concept of asexuality is necessary in understanding the concepts of demisexuality and gray asexuality.