The spot price is the current market price for one troy ounce of pure gold or silver, set continuously by global commodity markets (primarily the COMEX in New York and LBMA in London).
Spot vs Retail Price
You will never buy bullion at exactly spot. Dealers add a premium to cover minting, distribution, dealer margin and (for coins) sovereign mint costs. When you sell, dealers offer below spot for the same reason -- the spread is how they make money.
How Spot Is Set
Spot is the price of the nearest-month futures contract on COMEX, plus the London twice-daily fix. Outside of trading hours, electronic markets continue to set indicative prices.
Tracking It
Live spot prices update every few seconds on dealer sites like APMEX and JM Bullion. For free APIs: metals-api.com (limited free tier), GoldAPI.io, and Yahoo Finance ticker symbols GC=F (gold) and SI=F (silver).