A synthetic ETF represents some segment of a market or a market index, but doesn't invest in the actual securities. Typically this means they're using options contracts or similar instruments (swaps).
The most obvious of these are leveraged ETFs: they aim to return something like "twice the daily performance of the S&P500". Sometimes these are short ETFs: "twice the inverse of the daily performance". Because their objective is the daily performance, their returns may diverge significantly over time. They're pretty much always a good way to lose money in the long term. They're primarily used for day traders to have an effective way to perform certain day-trade strategies.
There may be other kinds of synthetic ETFs out there. I don't know about the details of them. There are definitely some commodities-futures funds that don't hold the actual commodities but I don't know any in the ETF flavor. Commodity-futures funds are subject to what they call contango in certain (rising) markets, which may hamper their ability to chase that performance. (They can't take physical delivery. If the price for delivery in 12 months is higher than the price of an option expiring now, then they can't actually capture that gain.)
You can tell a regular ETF by the fact that its prospectus and "about this fund" info which says what it invests in. A standard vanilla ETF will say something like "this fund invests all or substantially all of its assets in the common stocks of the companies in the Standard & Poor 500" (or whatever the ETF represents). These are the kinds of ETFs an individual investor should probably be investing in.