Allosexual and alloromantic (often abbreviated to allo if the person is both) is the opposite of asexual and aromantic. In other words, someone who experiences sexual or romantic attraction. The term was created by the a-spec community as a way to non-asexuals and non-aromantic, in the way the transgender individuals use the term cisgender to refer to someone who is not trans.
There are a group of people who claim that allo is a slur, saying that asexual people are calling them 'dirty' for experiencing sexual attraction, despite the fact the word allosexual is simply stating a fact, and is short hand for people who are not asexual.
Etymology
The prefix allo- means 'other' possibly meaning 'other than asexual'.