What is a rare 1 cent coin?

Could you please explain what is meant by a "rare 1 cent coin"? Are there specific years or mint marks that make a penny particularly valuable or uncommon? Are there any other factors, such as condition or metal composition, that contribute to a penny's rarity? I'm curious to know more about what makes a 1 cent coin considered rare and what collectors might look for when seeking out these types of coins.