Het refers to romance and/or sex between two characters of opposite gender. Like all kinds of fanfic, it can be very good when it's well written, but very often it is not. Often, at least one of the characters is some kind of Mary Sue, or otherwise very OOC. Bad het, especially when it is the sole driving force of the plot (if there is one), is dealt with by the Division of Bad Het.
When writers advise their readers of pairings in their summary, het pairings are often written the same way as slash pairings: Person A/Person B. In fact, "slash" may sometimes refer to any fic in which the romantic paring(s) are the focus of the story. However, usually this is not the case, and while many writers warn for slash, most do not warn for het. This can lead to irritation on the part of readers who aren't expecting to be confronted with romantic interactions, particularly when done poorly.
As stated above, het can be very well done, but it can also be very, very bad, especially in the hands of teenagers who know little to nothing about real relationships or the Mechanics. Bad het often suffers from being rapefic, hurt/comfort, or a bad lemon; it also may contain bad biology, horrific squick, dubious lube, etc.