Plain meaning
Start with the shortest useful explanation before going deeper.
An optional additional fee paid on top of the base fee to increase the likelihood that a transaction is processed quickly by the current leader, expressed as a price in micro-lamports per compute unit (CU). The total priority fee equals (compute unit price × compute unit limit) / 1,000,000 lamports. Leaders sort transactions in their queue by fee-per-CU, so setting a competitive priority fee is the primary mechanism for ensuring reliable transaction landing during congestion.