How pip value is calculated
A pip is the standard unit a currency pair moves in: 0.0001 for most pairs and 0.01 for yen pairs. Its value depends on how much you trade and which currency the pair is quoted in.
One standard lot is 100,000 units of the base currency. On EUR/USD that makes one pip 0.0001 × 100,000 = $10. If your account is in pounds, that $10 is converted at the current GBP/USD rate, so a pip is worth a little less than £10.
Why it changes between pairs
Pairs quoted in US dollars (EUR/USD, GBP/USD, AUD/USD) are worth $10 a pip per lot. Pairs quoted in another currency, like USD/JPY or EUR/GBP, are worth 10 units of that currency per lot, which then has to be converted. That is why a pip on GBP/JPY is worth a different amount from a pip on GBP/USD, even at the same lot size.
Gold is different
Most brokers quote gold as XAU/USD with 100 ounces per lot. Here one pip is taken as a 0.10 move, worth $10 per lot. Some brokers use 0.01 as the pip, so always check your platform's contract specification.
Why it matters for your risk
Your risk on a trade is pip value × stop loss in pips. If you don't know your pip value, you don't really know your risk. The lot size calculator works backwards from the amount you want to risk.