Requotes belong to the instant-execution model, where the client asks to trade at a specific displayed price and the broker must either accept or counter. If price has moved, you get a dialogue box with a new number and a few seconds to decide.
They are frustrating around news, when the price can move again before you respond. The alternative, market-execution, removes requotes but accepts slippage instead: you always get filled, just not necessarily where you expected.
Example: you click to buy EUR/USD at 1.0840 as a data release hits. Two requotes arrive, at 1.0845 then 1.0851. By the time you accept, entry is 11 pips worse, $110 on a standard-lot.
Related: instant-execution, market-execution, slippage-tolerance, last-look