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These attacks happen when the player/monster hits the AC exactly. If this happens the damage is reduced by half.
Example: The players AC is 18 and the monster rolls an 18 and then rolls 10 for its damage, that is a hit but it barely hits him causing the player to be able to glance the blow a bit resulting in half damage, so the player only receives 5 points of damage instead of 10.
These attacks happen when you roll at least 10 or higher than the targets current armor class. In result you are able to add an extra damage roll to the damage.
Example: The monster has an AC of 12, but the player rolls a 22. They then roll their damage of 1d8, but since its 10 more than the targets armor class they can instead roll 2d8.