The main purpose of mining is to secure the block chain. The reward is a the incentive for miners to exist.

Each block that gets mined means that in order to undo a transaction that was previously in the block chain, an attacker would have to mine a block before the network produced another block on the main chain.

So if your transaction was in block 33123, and the chain looks like

  block 41873 : [ parent : ... ]
  block 33123 : [ parent : block 41873 ]
  block 71282 : [ parent : block 33123 ]

then in order to undo block 33123, an attacker would have to produce three blocks:

  block 41234 : [ parent : block 41873 ]
  block 39834 : [ parent : block 41234 ]
  block 58762 : [ parent : block 39834 ]

before the network produced a new block on the main block chain. So the attacker would have to have 3x the computing power of the remainder of the network.