Mana burn
Mana burn used to be loss of life for not using mana in your mana pool when a phase ends. For instance, you tap a Swamp to cast Dark Ritual which gives you which you use to cast Erg Raiders (which cost ). If you can't use the remaining File:Manab.gif then you will lose 1 life from mana burn.
The rules update to Magic 2010 has removed this part from the game. Players do not suffer loss of life for unused mana any more.
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In-world meaning
In storylines mana burn happens when a wizard holds mana and doesn't use it to cast the spell. Such a wizard can seriously suffer from it, be killed, or even be burned to ash if the amount of mana was too big. Some victims of mana burn can be also turned to the Fallen.
For those who have been laid. Land and mana are two different things. Land cards are used to generate mana when taped. One mana added to your mana pool for each land taped unless an ability allows you to add more, normally, a non-basic land. Your mana pool is an imaginary representation of the amount of mana you have available for use to cast a spell. Should you miscalculate and add more mana than you will use, say, pay 8 mana to play a card with a cost of 7 you will lose one life. If you pay 10 mana and only use 5 then you loose 5 life. Because land and mana are not the same you would not loose land this way.