Complex Scripts
Embedding Segregated Witness inside P2SH
Let's assume, for example, that Alice's wallet is not upgraded to segwit, but Bob's wallet is upgraded and can handle segwit transactions. Alice and Bob can use "old" non-segwit transactions. But Bob would likely want to use segwit to reduce transaction fees, taking advantage of the discount that applies to witness data.
In this case Bob's wallet can construct a P2SH address that contains a segwit script inside it. Alice's wallet sees this as a "normal" P2SH address and can make payments to it without any knowledge of segwit. Bob's wallet can then spend this payment with a segwit transaction, taking full advantage of segwit and reducing transaction fees.
Both forms of witness scripts, P2WPKH and P2WSH, can be embedded in a P2SH address. The first is noted as P2SH(P2WPKH) and the second is noted as P2SH(P2WSH).