Tankering fuel means that an aircraft carries not only the fuel quantity required for the flight to the destination, but also the fuel, or a part of it, required for the next leg of the trip. The aircraft is therefore its own tanker.
Tankering means reduced cost
This practice can be used when the difference in fuel price at departure and destination airports makes the operation less expensive than refueling at destination. The time to refuel can be also a factor. More: The benefits of tankering considering cost index flying and optional refuelling stops.
From the previous article:
Fuel expenses remain one of the major components of an airline operational cost, depending on the aircraft size, it may approach from
20% up to 70% of its total flight cost.
Fuel tankering has been studied and applied by airlines at least since the oil crisis in the 1970 decade. It has become an excellent
fuel saving strategy for airliners proving costs reductions up to 10%.
Example of price difference in Europe:

Difference in fuel prices in Europe, source Eurocontrol
Example of savings by fuel tankering:

Savings by fuel tankering for airports distant by 300 NM. Eurocontrol
How to read: For a round trip between airports distant by 300 NM, if fuel is 20% cheaper at the departure airport, then by performing a full tankering, 45 kg of additional fuel will be needed, but this will save 196 € (8%) for the round trip.
Tankering means also more CO2
Tankering means burning more fuel than strictly required, this can provide an economical advantage, but this operation is usually not neutral for our environment, depending on how fuel is delivered to airports. From the study by Eurocontrol:
[...] it was estimated that fuel tankering could result in a net
saving of 265M€ per year for the airlines. However, it would
generate 286,000 additional tonnes of fuel burnt and 901,000
tonnes of CO2 emissions at ECAC level per year.
This represents about 2,800 round-trips between Paris and New York or
the annual emissions of a European city of 100,000 inhabitants.
(ECAC is the European conference for civil aviation)
Hence: