Heteroromantic simply means that one feels romantically attracted to members of the opposite sex. This is not necesarily to say members of the 'opposite' gender, as many people who identify as heteroromantic do not consider themselves part of the binary gender paradigm.
Generally, this term is used specifically to refer to people who identify as asexual. (Generally, if you are not asexual, your romantic orientation will match your sexual orientation, making such distinctions redundant). Because the majority of the human race is raised to see heteroromanticism as the default setting, it is often assumed that asexuals are heteroromantic (or perhaps aromantic, to mirror their asexualiy). However, there are certainly those who identify as homoromantic, biromantic, or panromantic.
A heteroromantic asexual will, generally, desire more or less the same romantic activities as a cisgendered person, but will not desire sex. Despite this being a very simple idea, it is a fairly radical concept for the average human, and asexuality, perhaps particularly heteroromantic asexuality, is more likely to be seen as a condition to be solved medically than are other sexual/gender identities, even within the the LGBTQ population.