"H-game" stands for "Hentai-game".
While most of these games have not this kind of content ("H"), these games are very popular has the normal sims themselves.
About this games...
The theme is almost the same on all of them. You're somekind of foreigner who is seeking job/studying on school and often bump with a wide variety of girls who end up falling in love with you.
Whenever the oportunity comes, you find yourself in "adult" situations with this girls, at different times and places, depending on how you handle the events you're put through.
--Article Written by: IceV--