The short answer
A Partially Signed Bitcoin Transaction, or PSBT, is a portable container for building and signing a Bitcoin transaction. It carries the transaction plan plus the information that signers may need, such as the outputs being spent, scripts and key derivation paths. Wallets can exchange the container without putting a private key on the same device that selected the payment.
A PSBT is not the transaction that miners confirm. It is a coordination format used before the final network transaction exists.
How it moves between wallets
A coordinator first chooses the inputs, recipients, amounts and fee. It packages that plan as a PSBT. One or more signers inspect it and add signatures for the inputs they control. The updated PSBT returns to the coordinator, which can combine contributions and finalize the transaction once every required signature is present. Only the extracted final transaction is ready for broadcast.
BIP 174 defines the original version 0 format and the roles in this process. BIP 370 defines version 2, which stores the transaction details as separate PSBT fields. Bitcoin Core 31.1 implements creation, decoding, combining and finalization operations in its PSBT RPC code.
For example, a two-of-three multisignature wallet can create one PSBT on a connected computer, move it to two hardware signers and collect their signatures. The hardware devices do not need to connect to the Bitcoin network, but each person should still verify the destination, amount and fee on a trusted display.
What it does not protect
A PSBT is not encrypted. Depending on how it was built, it can reveal previous transactions, scripts, public keys, extended public keys and derivation paths. Share it only with the intended participants and do not treat a QR code or file as harmless merely because it contains no private key.
The name also causes two common misunderstandings. A PSBT can contain no signatures, some signatures or enough signatures to finish the spend. “Partially signed” names the format, not a promise about its current state. And a fully signed PSBT is still a container: it must be finalized and extracted before there is a network transaction to broadcast.