Trending refers to price action that follows a relatively constant direction (up or down) for a given period of time (e.g. a long uptrend or downtrend). When a market is trending, there can still be peaks and valleys, but the overall direction is generally upwards or downwards, especially when you zoom out or look at the higher time-frames.
Ranging refers to price action that bounces inside of a horizontal channel (a lot of ups and downs within a given range). Typically, support and resistance is well-defined within ranging price action, but break-outs and fake-outs can still occur.