Passive investment management is a style of investing which tries to mirror the performance of a set benchmark, for example a stock market index, such as the FTSE 100 or the S&P 500.
Active investment management, in contrast, is where a fund manager picks the shares, attempting to beat a market (and passive funds) with their skill and judgement.
Passive investors believe in the "efficient market hypothesis" (stay awake at the back!), which states that the market incorporates and reflects all information at all times. If everything is known and reflected in prices, how do you get an edge?
Others say the efficient market hypothesis is nonsense. An additional benefit of passive management is that these funds are generally a cheaper investment. Sometimes it pays to be lazy.