What are 'El Niño' and 'La Niña'?

They are both sets of weather patterns.

El Niño is a weather phenomena which tends to occur in tropical waters of the Pacific Ocean. It affects the region across the Pacific from New Guinea to South America, known as the Equatorial Pacific. During an El Niño season, which occurs on average every 2-7 years, a shift in ocean currents and winds brings warm water towards the eastern Pacific, displacing the usual cold water that comes up from the ocean depths. As well as affecting marine life, the El Niño has an effect on weather patterns.

Under normal conditions, in the tropics warm oceans tend to be accompanied by heavy rains, resulting in heavy rains in the warm west Pacific while the cooler east Pacific receives far less rainfall. This is reversed during an El Niño, when the ocean temperature gradient from one side of the Pacific to the other weakens. Warmer than usual eastern ocean temperatures cause droughts in the west, while the unusually warm eastern waters bring heavy rains and floods to the Pacific coast of South America, which is usually much drier.

It's all a matter of interactions between the oceans and the atmosphere. Changes in sea surface temperatures causes a shift in air pressure which, in turn, can result in climatic anomalies, such as severe droughts, flooding and even cyclones. One of the effects is that the normal circulation patterns over the Pacific are disrupted, and moisture-bearing trade winds weaken, whilst drier westerlies increase.

El Niño has a number of effects, beyond causing droughts and floods on opposite sides of the Pacific. It causes die-offs of plankton and fish and affects Pacific jet stream winds, altering storm tracks and creating unusual weather patterns in various parts of the world. Scientific investigations of this phenomenon are ongoing, and it is yet to be determined whether El Niño is oceanic or atmospheric.

La Niña is the opposite to El Nino. It involves cooler than normal sea temperatures in the eastern part of the Pacific Ocean. This means that weather conditions, etc, are in reverse to those seen during El Niño.

Both phenomena are phases of warming and cooling in the Tropical Pacific Ocean. They cycle through after a period of years - the number is not precise and can range considerably compared to other phenomena like this - and usually have some warning signs the year before a change.

The names are derived from Spanish: El Nino is spanish for "boy" and La Nina is spanish for "girl".
Depending on the prevailing weather patterns, each is (respectively) a warmer than usual or colder than usual local ocean current off the western coast of South America.