Asexual (often shortened to ace) refers to someone who experiences little or no sexual attraction. Being asexual does not make someone incapable from experiencing romantic attraction, platonic attraction, or love in general. Asexuals can be of any romantic orientation including aromantic.
Asexuality is separate from abstinence and celibacy because the latter two are personal choices motivated by morals or religious beliefs while asexuality is a sexual orientation or lack thereof.
Although asexuals lack sexual attraction they can have sex to pleasure themselves/a partner or to have children.