Best execution is not a promise of the best price on every trade. It is a process requirement: the firm must have a policy, apply it consistently, monitor outcomes and be able to demonstrate it. In the UK and EU, firms must publish an execution policy and clients must consent to it.
For traders, the practical value is the paper trail. If fills are consistently poor, the execution policy and the firm's own monitoring data are what a complaint to the regulator or ombudsman is built on.
Example: a client's 60 market orders show an average 1.2 pips of negative slippage with no positive instances. Pure chance would produce some positive fills, which makes the pattern worth raising formally.
Related: slippage, hybrid-book, fca, last-look