In investing jargon, a "falling knife" is a seemingly good stock whose price is plummeting. It is a shorthand version of the old investing saw "Don't try to catch a falling knife."
When the price of a seemingly good stock starts to fall rapidly, investors may be tempted to buy the stock on the assumption that it will inevitably rebound. The admonition to avoid trying to catch the "falling knife" warns investors to hold off on purchasing the stock at least until the rapidity of its fall levels off or even until the price rebounds a little bit, because otherwise the investor has no idea how much further it may fall.
The reasoning is that on one hand, even good stocks may continue fall a long way in price once a vicious cycle of panic selling has been triggered for some reason, while on the other hand, the investor may have misjudged and this might actually be a bad stock that will never rebound.