A Horror check is a special type of Will check made at the beginning of combat against a monster. Only a single horror check is made with each monster per turn, no matter how many rounds of combat or evasion attempts ensue.
The investigator rolls dice equal to his or her Will statistic (skill value), plus any bonuses specifically for horror checks, modified by the monster's horror penalty, written as a blue number on the bottom-left of the monster marker's combat side. If the investigator rolls at least one success, nothing happens and combat begins. If the check fails, the investigator takes Sanity damage equal to the number of blue dots under the monster's horror modifier.
If a monster has no horror modifier, then investigators do not have to make a horror check when fighting it.
An investigator who successfully evades a monster does not have to make a horror check unless the monster has a special ability that states otherwise.