Before we get into what PSBTs are, let's refresh ourselves on how a traditional transaction works on the Bitcoin network.
Generally, when sending Bitcoin from one person to another, a message is digitally, cryptographically signed, and then broadcasted to the Bitcoin network. The broadcasted signed message is then validated by network nodes and recorded on the blockchain. Once the transaction is confirmed by the network, it is included in a block.
A Partially Signed Bitcoin Transaction (PSBT) is a Bitcoin standard that allows multiple people to pass around a single unsigned transaction and sign it before broadcasting it to the Bitcoin network. PSBTs separate the creation and signing of a transaction, enabling different people to execute different parts of the transaction to be broadcasted to the Bitcoin network.

In simple terms, PSBTs allow you to virtually shake hands with someone to execute a transaction.
If you are coming from the Ethereum ecosystem, you're most likely used to interacting with a smart contract, which acts as a decentralized, trustless, 'middleman' when "virtually shaking hands" or transacting with two or more people. Since smart contracts don't exist on Bitcoin, utilizing PSBTs is a great way to transact in a trustless fashion on the Bitcoin network.
However, as is often the case when interacting with cryptocurrencies, the UX for exchanging satoshis using PSBTs is poor.
You need to copy an unsigned PSBT into a wallet.
Cryptographically sign it.
Copy the signed PSBT and paste/send it to the person you are transacting with.
They copy the PSBT into their wallet, sign the other side of the transaction, and broadcast it to the Bitcoin network.
Bitcoin Ordinal marketplaces like OpenOrdex take advantage of PSBTs to enable users to buy, sell, and trade ordinals. You can learn more about Bitcoin Ordinal marketplaces and how they work by checking out my post here.

