Reinforced Anvils are more or less the same as normal anvils, with the exception of it costs a lot less levels to repair/rename equipment. The crafting recipe is 3 Heavy Iron Blocks and 4 Heavy Iron Ingots.
B = Heavy Iron Block H = Heavy Iron Ingot
The Reinforced Anvil has about the same uses as a normal Anvil, except it uses significantly less levels to repair or enchant. Also, The Reinforced Anvil does 2 Hearts of damage per block for anyone unlucky enough to have this fall on them. Some additional uses include you need a Reinforced Anvil instead of a regular one to repair/enchant Heavy Iron Tools, as well as Exo Tools.
There isn't much else to use this for.