The most common use of the word is when referring to a large ship, carrying petroleum products. Apart from pipeline transport, tankers are the only method of transporting large quantities of oil around the world.
Such tankers have several times caused large environmental disasters when sinking close to coastal regions, causing oil spills. See Exxon Valdez, Braer, Prestige for examples of tankers that have caused oil spills.
The largest tanker in the world is the Jahre Viking.
A tanker is an aircraft used for in-flight refueling. The US Air Force mostly uses converted transport aircraft, such as the KC-135 Stratotanker. The US Navy tends to use smaller aircraft, often converted attack aircraft such as the A-6.
A tanker is any crew member of a main battle tank.