It's kind of hard to define Crichton, as he appears a normal human. One way would probably be to describe how he differs from his crewmates.
Crichton is essentially our window on the Farscape universe. He reacts as more or less any other human would react, learns as we learn, and applies our knowledge, logic and human traits to many an unfamiliar situation.
John has wanted to be an astronaut since the age of 4 or 5 apparently, when man first landed on the moon (although this would make him about 37 years old now). His father, Jack Crichton, had had a long and illustrious career in the IASA space program, and he wanted to follow suit. It may be possible that the death of his mother may have had something to do with it.
Before leaving Earth John Crichton had been an IASA scientist and astronaut. Indeed, he had been on two shuttle missions and was working with his old schoolfriend and fellow scientist D.K. on a theory. This theory, if proved correct, would allow a craft to use a gravitational body such as a planet to slingshot it at previously unrecorded speeds. This would be a huge step in interstellar travel.
This was called the Farscape project, and John was going to prove the theory by actually going up into space and attempting the risky maneouvre using a specially-built craft, the Farscape 1 Module. He would be watched by D.K. and his father on the ground in mission control.
Taking his third shuttle ride, John's experiment appeared to be going well, until D.K. and his father radioed in to report some sort of radiation wave. However, the transmission broke up and John was sucked into this wave, which ended up to be a wormhole to the other side of the universe.
John was brought aboard Moya and greeted in a less-than-friendly fashion by her newly-liberated inhabitants, believing him to be a Peacekeeper. It was not long until they discovered he was something totally new to them, but it took time for him to earn their trust, eventually done by saving D'Argo.
Since then, Crichton has been looking for ways to get back to Earth, and has even found another wormhole before, but it proved too unstable to travel through. However, since his run-in with the Ancients, he has carried the knowledge to produce wormholes in his head, but too deep for him to even know it. This is why Scorpius has been after him, for the knowledge.
Crichton has proved a reliable ally to the crew of Moya, always ready to help and also use his ingenuity. He normally proves calm and collected in most situations, but is still trying to understand the universe around him.
However, he has gone through some odd periods recently when he was implanted with Scorpius's neural chip, when he started having visions of Scorpius. The chip has saved him before, granted, but it was not long before it attempted to take control of him, with limited success. As such, Crichton has had a few chances at killing Scorpius, but could not because the chip would not allow him to. Most recently though, the chip has been able to take control of his body completely, effectively killing Aeryn in the process.
With Aeryn resurrected by Zhaan though (at the eventual cost of her life), Crichton and Aeryn's relationship seemed rocky. The Scorpius clone remained in his head, now merely a tool (though an annoying one) to ask for advice.
However, John has been taking his wormhole obsession too far, once seeming ready to give up on Moya for prospective wormhole info from the Pathfinders. This eventually lead to Zhaan's death, though he got the impression Earth was nearby from an old Three Stooges clip caught by Pathfinder sensors.
Since being twinned by Karvok, the two Crichtons have lead different lives on Moya and Talyn. While the Moya Crichton was jealous of the one on Talyn with Aeryn, and one on Talyn dealt with finally being in love with Aeryn, and meeting her rather psychotic mother (who later committed suicide). With the Scorpius clone (aka Harvey) being removed (shortly after Harvey took control of him again), things seemed fine between Aeryn and the Crichton on Talyn. But with that Crichton dead (after being called by the Ancients to destroy Furlow's wormhole tech and alliance with the Scarrens), the other Crichton did indeed have a little jump for joy when Talyn met up again with Moya. However, Aeryn knows that Crichton is not the man she fell in love with.
Encouraged by the other Crichton's dying words, Crichton decided to set up a meeting with himself and Scorpius to destroy his wormhole development. Posing as to help Scorpius complete the wormhole tech to stop the Sebaceans being killed by Scarrens, the wormhole experiment was destroyed mainly by Talyn and Crais (at the cost of their own lives). But not before Scorpius told Crichton Earth had been found - just over 60 cycles of travel away. But with the wormhole equations unlocking in Crichton's head, Scorpius seemingly dead, and nobody after them, the rest of the crew decided to leave.
With the help of an old woman rescued from the Command Carrier, Crichton tried to imagine what would happen if he took his friends to Earth using the wormhole equations he was unlocking. If he took them though, disaster would follow. They wouldn't want to go to Earth anyway, each having their own objective - D'Argo wanting revenge on Makton, Chiana wanting to help her brother Neri, and Rygel wanting his kingdom back from his cousin Bishan. Aeryn also wished to leave to join an ex-Peacekeeper squad. Jool would stay with Moya until she found her home.
In the end, Crichton confronted Aeryn and they argued about whether they should stay together or not. At the toss of a coin, the decision was not.
And now, seeing his friends off in his module a short distance from Moya (who he would stay with), Crichton was greeted once again by Harvey, who gave him a present - the supressed memory of the old woman informing Crichton Aeryn is pregnant.
Calling Pilot, Crichton asked for them to give chase. Aeryn is out of comm range, Crichton's nearly out of fuel, and Moya has just been sucked into a wormhole. In short, Crichton's lost, once again, in the middle of absolutely nowhere.