Trap checks are hourly checks of your mouse trap. You can only receive trap checks for 24 hours since your last activity.
A particular hunter's hourly trap checks will occur on the same minute of every hour, but to reduce server load, not all hunters are assigned to the same minute. Trap checks may occur either on the hour or 15, 30 or 45 minutes past the hour. Trap checks are actually computed when a player returns to the game; so depending on timing, it is possible to see another player's profile where the hourly trap check has not yet been recorded, even though the player was taken along for a hunt by a friend's horn after the time of their designated trap check.
Mice caught on a Trap Check do not count toward Tournament scoring. One tactic in a tournament is to disarm cheese between hunts in order to skip the trap check, and thus avoid the situation where the trap check could break a streak or catch what would have been a high-point mouse at the wrong time.