I am new to investing in precious metals. I keep hearing the term "spot price" but I am not 100% sure what it refers to. Is that the price I pay for a coin at the shop?

Not exactly. If you ask what is spot gold today, you are asking for the price of raw gold on the commodities market for immediate delivery, usually in large bars. The coin price will always be higher because of minting costs and dealer profit. You can see the raw spot rate on sites like Gold Price Today to understand the baseline.