After a transaction is broadcast to the Bitcoin network it will be included in a new block that has been created and added to the blockchain through the mining process.
Once the transaction is added to the block it is said to have been mined at a depth of one block, or one confirmation. Two confirmations mean the transaction has been mined to a depth of two blocks, and so on.
To protect against double-spending, merchants & exchanges should set their own rules as to how deep a transaction should be mined before funds are considered confirmed – usually 6 blocks deep, but often much higher.