Where does the price come from?
Each time you tap "Get the live price and convert", the page requests the latest traded price for that pair from Binance's public market-data API (data-api.binance.vision) and converts with whatever it returns. The page stores no pre-written price data of its own; the number you see is the market price at the moment of the request.
One reminder: this is the last traded price on Binance's spot market, and it is only a reference. When you actually place an order there is a bid-ask spread and a fee, so your fill will differ; P2P merchant quotes usually sit a little off this price too. To see the order book and candles, go to the trading screen. If a click reports that the fetch failed, it is usually a network issue, so try again in a moment.
If you do not have a Binance account yet, once you sign up you can see full market data and depth right inside the platform. The sign-up guide takes about fifteen minutes to work through.