Supernatural is over eleven seasons deep at this point, so you may be wondering where to start watching. If you're planning to watch the entire series, I would definitely recommend watching everything in order because most season arcs are set up by the previous season arc. However, if you just want to know if the show's any good, I would recommend any of the numerous filler episodes. They can't actual stretch each story arc out to 23 episodes, so each season has several stories that feature the main characters working a side "case." Some of my favorites are The French Mistake (which isn't actually an independent case, but is awesome), LARP and the Real Girl, Ghostfacers, and Mystery Spot (which actually contains spoilers, but is hilarious). A Google search should reveal several lists if you want more.
The two main characters in the show are the brothers Sam and Dean Winchester, played by Jared Padalecki and Jensen Ackles, respectively. In the beginning of the pilot, their mother is killed by a demon when Sam is only six months old and Dean is just old enough to carry him out as the demon burns the house down. This incident reveals to them and their father the existence of various supernatural monsters (e.g. demons, werewolves, vampires, ghosts, & shapeshifters). Their father adopts the lifestyle of a "hunter," a human who hunts down these creatures and kills them. He raises them on the road, traveling across the country in their 1966 Chevrolet Impala, teaching them how to fight and kill from a young age. The first two seasons are spent hunting down the demon that killed their mother, starting when Dean picks Sam up from law school in the middle of the night. This then sets in motion a chain of events that more or less directly leads to the next several seasons.
The other main recurring human is the hunter Bobby Singer (not to be confused with one of the producers, who has the same name). Bobby is an old friend of the Winchesters and will often provide help, ranging from extra manpower, a place to stay, access to his library of supernatural lore, or use of his panic room. Since many hunters often pretend to FBI or other law enforcement agents using fake badges, Bobby has an array of phones and will pretend to be a higher-up back at headquarters when local law enforcement calls to check them out.
The fourth main character is the angel Castiel, played by Misha Collins. All angels are gifted with the powers of telepathy, healing, teleportation, time travel, telekinesis, and smiting various other creatures. They all carry a special blade, which is capable of killing any supernatural creature (who often can only be killed with a specific weapon or method) and are the only way of killing another angel. Another way to defeat an angel is to paint a siglum in human blood and press a hand to it, which forcibly teleports the angel away and temporarily prevents them from returning. They can also be trapped inside a ring of burning holy oil. Angels are by nature incorporeal and must inhabit a human host in order to interact with humans without injuring them. Angels come in three different power classes: the low-levels, serephs, and the four archangels (Michael, Lucifer, Raphael, & Gabriel). We first meet Castiel in the season four premiere, when he and a task force of other angels rescue Dean from hell. Fans have marked Castiel as one half of the show's few major (non-canon) romantic relationships, Destiel, alongside Dean.
The two other major recurring characters are the demons Meg (played by Nicki Aycox & Rachel Miner) and Crowley (played by Mark Sheppard). Demons are gifted with the powers of telekinesis, telepathy, and teleportation. Certain demons, known as crossroads demons, have access to a vast array of magic, which they will use to perform favors for humans who summon them (via a spell performed at a crossroads) in exchange for their soul after a period of ten years. Demons are actually human souls who have been tortured in hell for centuries until there is nothing left but evil. Like angels, demons must inhabit a human host. However, unlike angels, who must have a host's permission to enter them (though they don't seem to need to specify what they need permission for), demons can shove their way into anybody they want by brute force (even occasionally an angel). One thing hunters will often do when going up against a demon is trap them inside a special symbol (usually spray-painted on the floor) called a devil's trap and chant a spell which will exorcise the demon from the host and send them back to hell. Demons can only be killed by special blades (including angel blades), a special gun built by Samuel Colt (which is capable of killing almost anything), certain spells, or the powers of particular beings. However, they can be injured by exposure to iron or holy water.
Other monsters featured in the show include vampires, werewolves, shapeshifters, and ghosts. Vampires are created when a human drinks vampire blood and can only be killed by decapitation. Werewolves are created when a werewolf bites a human and can only be killed by a silver bullet or blade. They are prone to feasting on human hearts. Shapeshifters can take on the appearance of another human and can only be killed by a silver bullet or blade through the heart or decapitation. Ghosts are human souls who are trapped on Earth after death because of unfinished business or a traumatic death. They are dealt with by salted and burning the body. If the body has already been cremated or that doesn't work, there's usually still some piece of their DNA sitting around somewhere. Both ghosts and demons are unable to cross a line of salt and hunters typically use shotgun shells of it against them. Other entities including God, the Darkness, the four horsemen, leviathans, and various pagan gods appear from time to time, as well.