Ah, the most icky of xenomorphs. A facehugger (or Ovomorph, as occasionally described), is a chitinous spider-like beast that emerges from an Alien egg when close proximity to a living organism is detected. It has eight bony legs and a powerful long tail, which it uses to propel itself towards its unlucky victim. The aim of this attack is to clamp onto the face of said creature, which in itself, is not a pleasant experience, as the 'hugger holds hard with its appendages (hard enough that tearing it off will probably take the face with it), and will also proceed to strangle the victim, causing it to lose consciousness.
Once this happens, it's unfortunately not quite the end for the poor bugger, as the facehugger will then extend a long proboscis down the creature's throat and implant a chestburster embryo there. The proboscis also serves to supply oxygen to the host. During this time, the outer shell of the 'hugger will solidify, making detachment even more difficult. At this point, it's also worth noting that shooting or cutting a facehugger off of someone is probably a Bad Idea™ as the unlucky victim is quite likely to get a face full of lovely acidic alien blood. We're not talking a minor itch like you got from the NaOH back in labs, this is more of an "Oh my god, it's eating right through my fa-*gurgle* *thud*.
What has happened here is pretty much the facehugger's only purpose to exist. After safely implanting the embryo, the 'hugger will detach and die. The host will wake up shortly afterwards, groggy, confused, and in deep trouble. The poor sap will start to experience a sore throat, nausea, and hunger with increasing intensity, and towards the end, nosebleeds and chest pains. See, the gestation period of the xenomorph embryo is fairly short (1-24 hours-ish), and when it reaches maturity, it doesn't wait around to find a convenient door. It makes one. Generally in the victim's chest. In a cloud of viscera and gore, it bursts forth from the chest of the host, killing it fairly soundly, and scampers off to find somewhere cozy to grow up and eat people.
Now, luckily, all is not lost for a victim after they get a frenchie from hell from a 'hugger. There can be enough time to get to medical facilities, and there, be operated upon and have the embryo removed, or failing proper facilities, cryogenically frozen until a more convenient time.
Y'know, the best way of avoiding a gaping hole in chest though?
Duck when the little bastards leap at you.