Synthetic ETF
  
See: Exchange-Traded Fund (ETF).
ETFs provide a way to track individual indexes or sectors. They trade like stocks; you can buy and sell them throughout the day on the major exchanges. It's a way to bet on, say, the biotech sector, or Russian green energy stocks.
ETFs are products created by financial companies that hold the actual stocks involved (all the Russian green energy stocks in the index, for example). Then they issue the shares of the ETF to the market.
Synthetic ETFs do the same thing, except the structure is completely different. Think of it like those hardwood floors that aren't really made of wood (they're made of plastic or whatever). They do the job of keeping you from falling through the floor, while looking like wood...but the basic makeup is completely different.
Just like the real thing, synthetic ETFs allow you to bet on an index or sector. Only they do this by using derivatives. The companies selling these products don't actually hold the stocks involved (like happens with a regular ETF).
The main reason to use a synthetic ETF is to track a sector or index that doesn't have an ETF following it. It provides a way to simulate an ETF-like experience, even when no traditional ETF exists.