The Falcon is the main battle tank of the Eldar, capable of being equipped with a variety of weapons such as pulse lasers and shuriken cannons and doubling sometimes as a troop transport. Due to either the Eldar or Games Workshop being lazy, all Eldar tanks have the same body as the Falcon, just as the super-heavy Scorpion. (Because the Imperium has such a diverse and creative collection of chassis for their vehicles.)
Snarking aside, the Falcon occupies a similar slot in the Eldar army to the Razorback Transport, which is to say a very specific niche. Since Falcons aren't bought as dedicated transports they can be used as emergency transports, but with only six passenger slots and no fire points. This option only exists for a circumstance that may or may not occur and is impractical at best. The Falcon faces two other problems: firstly, while the scatter laser they have by default means their other main weapon is fairly accurate, said scatter laser/heavy weapon/shuriken cannon (at best) load out isn't getting its points back in kills compared to a dedicated infantry or tank killer. The second problem is that like so many options in the Eldar lists it's competing for a slot and/or points against Wraithlords and Wraithknights.
A big and obvious bright side is the anti-gravitic generators, which give the Falcon its amazing speed and agility are prime examples of the Eldar's technological mastery. Thanks to these powerful devices a Falcon can achieve speeds of up to 800 kph and soar to altitudes much higher than the equivalent Imperial craft, giving it limited flight capability. The Falcon's crew of pilot and gunner will themselves be veteran pilots, having learned their craft either on Eldar Jetbikes or along a similar Path, and take full advantage of these abilities.
Unfortunately, thanks to a certain Irish gremlin, a Falcon can just be as susceptible in being disabled with a simple rock in its engines. I guess it was a bad idea to design a tank with such an obvious weak spot eh?
in game terms its a very dangerous target for the high cost: you get a tank that can zip around the battlefield, is packed full of aspect warriors and nothing above s8 hurts it(making a mockery of your lascanons and railguns) and in ye olden days (7th ed backwards) it could punch right through a terminator squad with its ap2 starcanonn.
From a lore perspective its name is a rough translation of Faolchu, who was the consort of the Great Hawk that retrieved Vaul's sword and gave it to one of the Eldar hero bigwigs during the War in Heaven.