Receiving notification of a payment is almost instant with Bitcoin. However, there is a delay before the network begins to confirm your transaction by including it in a block. A confirmation means that there is a consensus on the network that the bitcoins you received haven’t been sent to anyone else and are considered your property.
Once your transaction has been included in one block, it will continue to be buried under every block after it, which will exponentially consolidate this consensus and decrease the risk of a reversed transaction. Each confirmation takes between a few seconds and 90 minutes, with 10 minutes being the average.
If the transaction pays too low a fee or is otherwise atypical, getting the first confirmation can take much longer. Every user is free to determine at what point they consider a transaction sufficiently confirmed, but 6 confirmations is often considered to be as safe as waiting 6 months on a credit card transaction.