In investing terms, catching falling knives means buying a stock that have had huge, quick drops. These drops often occur because something catastrophic has happened; accounting scandal, a product that has inadvertently killed someone, etc.
Playing the falling knives game is totally emotional in my opinion. Think about it…you see a stock that recently was $130 per share and now is falling and is and is trading at $80, then $70, the $60, and so on. What a deal this must be. The problem is that you never know when the bottom will be. Think about Nortel - once it traded at around $120 and now trades at between $3 and $4 per share. I am sure there were tonnes of investors who bought all the way down.
One thing that I try not to do is to buy against a trend. Things in motion tend to stay in motion and stocks are no different. If you want to buy something that has dropped dramatically, do your research to ensure the stock is still viable and wait until the trend starts to go the other way. This way you (hopefully) will limit your downside and make a nice potential gain on a turn-around play.