In fragmented markets the same instrument trades on many venues at once. A router checks where size actually is, accounts for maker rebates and taker fees, and splits the order so the combined fill is better than hitting one venue.
Routing decisions can quietly conflict with your interests. Routing for rebate capture rather than fill quality, or posting to venues where fill probability is low, produces worse execution that is invisible unless you measure arrival-price-benchmark by venue.
For most traders this is the broker's job, not theirs. The useful action is to read the broker's routing disclosure, ask whether payment-for-order-flow influences the destination, and compare realised fills against the prevailing quote.
Related: execution-algorithm, payment-for-order-flow, quote-data, latency