Homoromantic simply means that one feels romantically attracted to members of the same sex. This is in contrast to heteroromantic, biromantic, panromantic, and aromantic... and others as needed.
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). It is usual for people to equate 'homoromantic' with 'gay'/'lesbian'. The difference is that a homoromantic asexual will not have a desire to have sex -- a difference that is very important to the majority of the human race, and can be very alienating, even among a group (the LGBTQ population) that is very familiar with unfair alienation.