A refurbished engine is another engine (identical to yours) where all needed to be replaced parts were (still hopefully) replaced.
The difference is that (it really depends on a case by case basis) your engine might need less parts replaced and the replacement is done by your local mechanic (all in all it can cost less in some cases).
With refurbished engines all parts in a given list are replaced, no matter their current condition, and the replacement is done by workers that usually do everyday exactly that.
The cost of a refurbished engine (you give them back yours that they will refurbish for next customer) can be a little less (including transport costs) because the refurbisher has spare parts cheaper due to quantity and personnel is faster (because they do this specific work everyday and have all the proper tooling) but often it is very similar.
Your advantages with a refurbished engine are that it is generally faster than a local rebuild, and usually you are offered some kind of warranty (which may not be the case for a local rebuild).
For a company, it is a way to minimize the stop of the vehicle and to place some responsibilities to the external supplier.