An unconfirmed transaction lives in the mempool, visible but reversible. Inclusion in a block is confirmation #1; every block mined on top makes rewriting history exponentially more expensive, which is why receivers scale their demanded confirmations to the amount at stake.
The famous "6 confirmations" is a convention, not a rule — coffee sellers take 1, some exchanges want more. The full timing story (and what to do when you're stuck at zero) is in how long transactions take.