The horrors referred to in this question are the horrors that Katniss and her group of tributes experience whilst inside the arena, and it is clear that they are significantly terrifying in order to amuse and excite the audience in the Capitol and in the other Districts. During the course of the story the reader and Katniss discover that it is the result of a clock structure that causes one horror to be unleashed in each area of the arena per hour. The first horror Katniss experiences is a mist that burns, and claims the life of Mags when Finnick is unable to carry her any more. Secondly, there is the assembled masses of mutts that are monkeys, described as follows:
Fangs bared, hackles raised, claws shooting out like switchblades. I may be unfamiliar with monkeys, but animals in nature don't act like this.
Lastly, the major horror that Katniss and Finnick have to deal with is when they are trapped in the area with the jabberjays that seem to call out the names of those who are nearest and dearest to the tributes. In the case of Katniss this is Prim, but for Finnick it is Annie. These are the three horrors planned by the creators of the arena for the special quarter quell.