After you send, your transaction travels to the nodes, which check it and keep it in their mempool. Miners pick it up when its fee is high enough.
One confirmation
When a block containing your transaction is mined, your payment has one confirmation. On average a block arrives every ten minutes, but it can take one minute or an hour: blocks are found at random.
More confirmations, more certainty
Every new block added on top makes your payment harder to undo, because changing it would require redoing all that work. Many services consider a payment final after 3 to 6 confirmations; for a coffee, zero or one is usually enough.
Watching it happen
Your wallet gives you a transaction ID, or txid. Paste it into a block explorer website to watch your payment wait in the mempool, enter a block and gather confirmations.
▶ SEE IT IN THE MACHINEMINING is where a block is found; then BLOCK HASH seals it and BLOCKCHAIN locks it into the chain.