If EUR/GBP is quoted away from the level implied by EUR/USD and GBP/USD, a trader can convert euros to dollars, dollars to pounds, and pounds back to euros, ending with more than they started. The act of doing it pushes the three prices back into line, which is why the cross-rate stays honest.
In practice these gaps last milliseconds and are captured by automated systems co-located near matching engines. Retail platforms cannot reach them, and the bid-ask-spread on three legs usually exceeds the mispricing.
Example: EUR/USD 1.0840, GBP/USD 1.2700, so EUR/GBP should be 0.8535. A stale quote shows 0.8555. Selling EUR 1,000,000 at 0.8555 into pounds, then pounds into dollars, then dollars into euros returns about EUR 1,002,340, a EUR 2,340 gain before costs.
Related: cross-rate, latency-arbitrage, interbank-market, liquidity-provider