Merriam-Webster defines “asexual” as meaning “not having sexual feelings toward others; not experiencing sexual desire or attraction.”

The Asexual Visibility and Education Network (AVEN), which hosts an online community and archive of resources, has a more detailed description of asexuality:

An asexual person does not experience sexual attraction – they are not drawn to people sexually and do not desire to act upon attraction to others in a sexual way. Unlike celibacy, which is a choice to abstain from sexual activity, asexuality is an intrinsic part of who we are, just like other sexual orientations. Asexuality does not make our lives any worse or better; we just face a different set of needs and challenges than most sexual people do. There is considerable diversity among the asexual community in the needs and experiences often associated with sexuality including relationships, attraction, and arousal.

Does this mean people who are asexual can experience attraction to other people and form relationships?
Just as is the case with all people under the LGBTQIA+ umbrella, there’s no one universal experience. People who are asexual generally don’t experience sexual attraction to other people, but that doesn’t mean they can’t find someone attractive or that they don’t want to be romantically attracted to another person.

How can an asexual person be attracted to someone if they’re not sexually attracted to people?
Quite easily, it turns out, because there’s more to attraction than just sexual attraction. As AVEN explains on its website:

Many asexual people may experience forms of attraction that can be romantic, aesthetic, or sensual in nature but do not lead to a need to act out on that attraction sexually. Instead, we may get fulfillment from relationships without sex, but based on other types of attraction. Romantic attraction is the desire to be romantically involved with another person. Aesthetic attraction is appreciation for a person’s appearance. Sensual attraction is the desire to engage in sensual (but not sexual) activities with a person, such as cuddling, hugging, or kissing.

If an asexual man is not sexually attracted to another man but is romantically attracted, what would that mean? Does that make him both asexual and gay?
AVEN’s resource page explains that among some people who experience little to no sexual attraction, they might use one label for their sexual attraction, and another for their emotional attraction:

These people may still identify as lesbian, gay, bi, or straight. The split attraction model has led some people to identify separate sexual and romantic attractions. For example, a person who’s asexual but wants relationships with the opposite sex may identify as a “heteroromantic asexual.” Most sexual people may not view their orientation that way, and may simply combine their sexual and romantic attractions into one characteristic if they’re aligned. Asexual people often feel the need to specify both sexual and romantic attractions to make it clear what drives them and what they’re seeking from other people.

Does this mean asexuality is a type of sexual orientation?
That’s been up for debate. In a 2014 blog post for Psychology Today, Stephen J. Betchen wrote that the topic of asexuality is “highly charged” among people who study sexuality, in part because they cannot agree what it is:

One camp of sexologists’ claim that it is, and should be recognized as a major sexual orientation like heterosexuality, homosexuality and bisexuality are. The other camp sees it as nothing more than low libido.

In a 2015 article for Mic, write Julie Zeilinger explained that some people treat asexuality a spectrum of sorts:

Even among asexual people, there are a spectrum of identities. Demisexuality, for instance, is “a sexual orientation in which someone feels sexual attraction only to people with whom they have an emotional bond,” according to the Demisexuality Resource Center. They may “think of themselves as halfway between asexual and sexual,” [sexuality educator Sari] Locker added.

AVEN’s website says that among people who identify as asexual, there will be people who have little to no libido, as well as people who have libido but no desire for a partner:

Both types are equally valid in identifying as asexual, as sexual orientation is about attraction and desire towards other people, rather than strictly physiological reactions.

How will I know whether someone uses the term “asexual,” “demisexual,” “heteroromantic,” or any of these other terms?
As is often the case, it’s best not to use a word to describe people until you know that’s the word they would use to describe themselves and that they would be comfortable with others using for them. Some people use the term “ace” as short for “asexual,” but not everyone will use that term to describe themselves.