Non-native plant species are those that are not believed to be local to the area and often come from far-flung locations.
They've either got here accidentally (like seeds blown on the wind) or by deliberate planting. Some of these invaders can be very damaging to local plants - out-competing them for food or light for example. Japanese Knotweed is a famous invader species. It grows very high (2-3 metres), with very long roots and is therefore highly skilled at taking over areas very quickly. It also thrives on disturbance - natural or human - spreading to new areas with great ease.