An outburst flood is, quite simply, a flood caused by water bursting out of, or through, the barriers containing it.
Usually, the term outburst flood refers to a glacial lake outburst flood, AKA a jökulhlaup. It may refer to other floods caused by the breaking of a natural dam, but a natural dam generally means a moraine dam, a mass of rocks and dirt originally formed by a glacier, even if the glacier has long since melted. The flood is caused when a lake of meltwater at the base of a glacier breaks its banks, and floods into the surrounding areas. This might happen as a result of volcanic activity, icefalls and avalanches, an earthquake or ice quake, or a simple buildup of water pressure as the glacier melts into the lake.
Natural dams can also be caused by lava flows, in which case they are called a lava dam outburst flood. While glaciers, and consequently jökulhlaups, are common enough throughout the world, lava dams are much less common, and are mostly of interest to geologists. Lava dams may occur when lava spills into the path of a river, cooling and forming a blockage. They may be stable, but often they are based on the loose rock of the river bottom, and can suddenly break, sending tons of water and rock debris down stream. This sort of dam is more likely to form in canyons and deep river valleys, where the river cannot flow around the dam; the Grand Canyon in Arizona has had a number of these in its geological history.
Mars may also have had outburst floods; it has channels eroded onto its surface that match the channels formed by Earthly outburst floods. These 'floods' were most likely caused by subsurface pockets of CO2, or mixed CO2 and water. They formed in high-pressure pockets in the Martian rocks, exploding out in violent washes that scoured the surface before evaporating.