Damnatio Memoriae is a latin phrase, and its meaning is 'damning of memory'. In effect it was any particular law which punished all reference to specific individuals (or events). An example of that would be the Ephesian decision to ban the mention of Herostratos' name, cause he tried to burn the tempe of Artemis at Ephesos (one of the seven wonders) so that he could be remembered for this act 
Legend has it that he burned the temple the same day that Alexander the Great was born, and so Artemis herself was busy observing the infant Alexander, thus could not save her temple
Herostratos was obviously sentenced to death, but in later centuries his name was written down by historians, including Strabo, so the damnatio memoriae in effect was cancelled..
Another example could be the fine imposed on Aeschylos following his play 'The Persians', which caused so much grief in Athens that it was banned from being shown again. Aeschylos, of course, had even fought in the battle of Marathon, which he regarded (as is shown in his epitaph) as his highest achievement.
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You can mention other examples of this damning of memory, from historical periods
Legend has it that he burned the temple the same day that Alexander the Great was born, and so Artemis herself was busy observing the infant Alexander, thus could not save her temple
Herostratos was obviously sentenced to death, but in later centuries his name was written down by historians, including Strabo, so the damnatio memoriae in effect was cancelled..
Another example could be the fine imposed on Aeschylos following his play 'The Persians', which caused so much grief in Athens that it was banned from being shown again. Aeschylos, of course, had even fought in the battle of Marathon, which he regarded (as is shown in his epitaph) as his highest achievement.
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You can mention other examples of this damning of memory, from historical periods
