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nothing its free
Minecraft does not charge you to run a server for the game. You will, however, have to posses a computer to be the server. Otherwise you will have to rent a server to run for you, which costs money.
You can host a Minecraft Server from your computer for free (although you have the cost of internet upload). But, if your computer isn't powerful enough you can hire a server for an amount of money.
If you host a server at your home or etc., then it is free. But if you host it at a site (eg: verygames), then it costs money.
A dedicated Minecraft server is a server where you can play original Minecraft. Usually without plugins or mods.