How do oceanic lateral offset procedures work?
On high-altitude North Atlantic flights, planes can fly zero, one, or two miles to the right of the centerline of your assigned track. The offset is randomly selected. This is called Strategic Lateral Offset Procedures.

It's used in the oceanic flights or flights over remote land where there is typically no radar service, and ATC cannot "see" traffic separation. It provides, on average, additional horizontal separation between planes reducing the likelihood of midair collision and high altitude wake turbulence (which can occur as a result of RVSM).

Strategic lateral offsets can be authorized in en-route oceanic or remote continental airspace. The decision to apply a strategic lateral offset is the responsibility of the flight crew, and only where offsets have been authorized by the ATS and when the aircraft is equipped with automatic offset tracking capability.

https://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/enroute/oceanic/documents/WATRS_Plus/DOC_4444_16.5_SLOP_25Feb2011.docx