The base-fee buys eligibility; the priority fee buys position. Producers sort candidate transactions by the tip on top of the base fee, so a higher tip means earlier inclusion when blocks are full.
Tips matter most when timing has value: claiming an airdrop, avoiding an on-chain-liquidation, or beating others to a mint. They are also the currency of mev competition, where searchers bid tips away to win a profitable ordering.
Example: a swap using 150,000 gas at a 25 gwei base fee and a 2 gwei tip costs 150,000 × 27 gwei = 0.00405 ETH. Raising the tip to 20 gwei makes it 0.00675 ETH, an extra $8 at $3,000 ether, for a place near the front of the block.