A transaction is "confirmed" when it is included in a new block. Transactions that have not yet been incorporated into blocks are considered unconfirmed. If the transaction belongs to a block, it is considered confirmed.
As new blocks are added after the block to which the transaction belongs, it is confirmed further.
For transactions with low commissions, it can take time to get included in the block and they may remain unconfirmed for a long time.
Confirmed transactions are confirmed even if they are on orphan blocks. However, orphan block branches usually grow to only about two blocks, so they only have two confirmations.
In general, a transaction is considered almost certainly safe if it has six or more confirmations. However, there have been cases where operators' system failures caused transactions with six authentications to be rolled back, so it is important to choose a secure operator.