Flying on one engine
Transport Category airplanes (e.g., commercial jets) have performance limitations that are different when operating on one engine versus two engines.

Regulatory requirements for commercial operations require that a flight in a two engine transport category airplane be planned to be successfully flown if one of the two engines fail. 

The issues are fairly complicated, but the airplane must be configured and operated considering all existing circumstances (airport/runway/weight, etc.) so that if one of the two engines fails at the most critical time the flight can be continued to a safe landing at the original departure airport, the planned destination, or a suitable alternate airport.

For example, if you are departing Chicago in a B757 and the weather is so bad that although takeoff is allowed, landings are not, and an engine failure occurs (just as the aircraft is lifting off the runway) the capability of the airplane must allow an obstacle free climb, enroute and approach to a pre-planned alternate airport on a single engine.

Another example, if you are halfway between San Francisco and Hawaii in a B767 and an engine failure occurs, the airplane must be able to return to SFO or go on to some place in Hawaii on the remaining engine. (the technical components are a bit more detailed than my simple explanation, but the outcome is the same)

Most trans-ocean flights today are done in two engine transport category airplanes (e.g. B767/777 or similar) and the design criteria (see FAR Part 25) are such that continued operation after a single engine failure, if properly considered in the performance planning for the flight (which needs to happen), ensures a safe continuation to a suitable airport.

Of course, the single engine operational profile will be different (altitude, speed, etc.)