First, the boring stuff. Chlorine trifluoride is an interhalogen compound, ClF3, which is produced by fluorinating chlorine at high temperatures and was first synthesized in the 1930s. It is a colourless gas with a suffocating odour. It is known for being exceptionally and violently reactive, more oxidising than oxygen, and really, really, toxic. Its uses are in nuclear fuel reprocessing and semiconductor manufacture, though other uses were contemplated, in the past. There is a pretty strong case to say it's one of the most horrifically dangerous substances known to man.
Simply referring to it in material safety data sheet terms, though, doesn't do this wonderfully psychotic compound any real justice, though. It's all very dry and clinical, isn't it. So. Let's have a brief account of what all this means in the real world.
Well, firstly, it is hypergolic with almost anything. This means it will react so violently on contact with just about anything that it will cause stuff to catch fire that doesn't normally catch fire. It will set sand on fire, as sand, being mainly silicon compounds, will find itself rapidly fluoridated. Similarly, it will set on fire concrete, bricks, and even asbestos, which are all also silicon compounds. When I say it will set these things on fire, it won't just look like it like how if you set light to a pool of petrol it looks like the floor's burning. It actually causes them, themselves, to burn. It also reacts explosively with water, and its reaction products (depending on the amounts of each substance involved) include such lovelies as hydrochloric acid, hydrofluoric acid, fluorine gas, and chlorine gas. It also will fluoridate most metals including otherwise seriously unreactive platinoid metals (palladium, platinum, osmium, iridium, etc.) and corrode them, and if any metal object it comes into contact with is at all rusty, the rust will probably catch fire.
It's also toxic either by being breathed in or absorbed through the skin, but if this happens you're probably more preoccupied with OHFUCKOHFUCK I'M ON FIRE HELP HELP HELP! Also, at higher temperatures it spontaneously decomposes into chlorine gas (toxic), and fluorine gas (corrosive, and toxic.)
For all the above reasons, in the 1930s, the Nazis experimented with it as a weapon of mass destruction. This is because a ClF3 shell or bomb fired at a bunker, say, would cause said bunker to catch fire, and its inhabitants to catch fire, dissolve, and be poisoned in that lovely green-frothy-phlegm-coughing way that chlorine poisoning engenders. Not only that, but you know how I mentioned that it reacts on contact with water to form hydrochloric acid and hydrofluoric acid? Well. Humans are 70% water so it would react with moisture in the body (explosively) and leave those products behind. Hydrochloric acid is, of course, corrosive to flesh, but hydrofluoric acid is even worse as it simply soaks through human flesh and attacks one's bones, melting them from the inside out, as well as being highly toxic in its own right. Further, a ClF3 bomb let off in a populated area would result in fires that get worse when sprayed with water or water-based foam and, given that ClF3 is a better oxidant than oxygen by mass, even a carbon dioxide extinguisher would be of little value. Not to mention the effects on enemy morale of seeing one's comrades burnt alive on contact and actual concrete burning.
However, this fantastical dangerousness is exactly why it was never deployed in battle. Nerve gas, for instance, is horrifically toxic and even a small amount results in a painful, seizure-laden bowel-voiding death, but at least it doesn't set fire to everything it contacts. Chlorine trifluoride can be stored in metal containers that have been treated with fluorine gas to begin with as that then leaves a layer of aluminium or iron fluoride on the inside which sticks to the body of the tank and acts as a buffer but if that is compromised, the container may spontaneously explode. The OSHA in the US delightfully says of this, "Ruptured cylinders may rocket." Needless to say, it was considered just as much a danger to one's own side and plans weren't really followed up.
Attempts have been made also to use it as a rocket fuel as, being more oxidising by mass than oxygen, this would mean that one's rocket need spend less of its weight on propellant. Unfortunately the same problems apply and, had Apollo 11 exploded on the launch pad, set fire to Cape Canaveral and poisoned all its inhabitants, NASA would have found its funding pulled in a second.
It does have some industrial uses, as I have said, in semiconductor manufacture and nuclear fuel reprocessing and there are places where you can buy it. However, you are strongly advised to read this before so doing, as it not only tells you exactly how to handle it without being poisoned or set on fire, but also it has some pictures of it being sprayed it at things to see what happens (this is also not advised.)
Finally, let's all just hope that a terrorist doesn't get their hands on this stuff, especially not with the Olympics round the corner.