Transactions with segwit inputs have a witness section. While non-segwit inputs have their script arguments in the input script, for witness inputs, the script arguments and witness scripts go to the witness section. Witness data is only parsed once when a transaction is validated, and then never needs to be revisited except to provide peers old blocks. Thus, it’s a lot less costly for nodes to maintain than output data which needs to be kept in the UTXO set until the UTXO is spent. Witness data is discounted to reflect this lower cost and to reduce the cost of inputs in comparison to outputs to encourage good stewardship of the UTXO set.

The idea behind Inscriptions is to write data into a part of a P2TR input’s witness stack that is not relevant the payment authorization as a way to publish something directly on the blockchain. This is generally extremely inefficient and expensive, and will hopefully soon be priced out.