Clients don't verify transactions, Miners include them in a block.

Basically you transaction gets only confirmed 1 Time. After that it counts only the numbers of blocks over the block that confirmed your transaction.

The reason for this is, that the client counts always the longest string of blocks in existence as valid, so which each block more it becomes harder to override your transaction.

This was the easiest way I could explain it.

Edit: That should explain it:

http://spectrum.ieee.org/img/06Bitcoin-1338412974774.jpg