When Castiel made his first appearance, the show had no proof of actual angels. There were demons aplenty but angels had never been seen and rarely spoken about, until Dean and Bobby Singer summoned the creature that pulled Dean from Hell at the beginning of season four.
Castiel was imposing, blacking out homes, causing shifts in the wind patterns, and sending electrical sparks into the air. The two hunters had no idea what to expect and so they threw everything at him, but he remained unscathed and not bothered by their attempts.
In the fourth season, the first season with the character Castiel, he is seen as quiet and reserved, almost robotic; making decisions based upon rationale and orders from Heaven.
Additionally, he is the only character in the show that has been an angel, human, the Devil, and a god since his appearance. Once he fell from Heaven, after siding with the Winchesters and by extension humanity in the war between Lucifer and Michael, Castiel came to respect humans more than his other angelic counterparts.
His stay on the show was supposed to be temporary until the fans made it known that they adored Castiel. He remains an integral part of the show today (rumored for the 14th season, but nothing confirmed).
Since he ingratiated himself into the human world, Castiel had difficulties grasping pop culture references, sarcasm, and many of the idioms we use, and that is what makes him inadvertently funny. Dean once likened him to a "baby in a trench coat" because he was so new to human communication. But be careful, that baby will smite you where you stand without blinking.
Walking around with an angel was a chore to Dean Winchester at one point (cue the eye-roll). Dean wasn't a believer, despite his mother's attempts to reassure him that "angels are watching over you." After seeing so much pain and suffering in the world and in his own life, Dean was not a believer in God and even less so in angels.
After months of constant partnerships and reliance, Castiel has become the best friend Dean ever had. There is no person other than Sam that Dean trusts more to watch his back or protect his brother.
The relationship between the human and angel makes for a great buddy comedy. In fact, the picture above describes the relationship perfectly: Castiel screwing up a mundane human task, and Dean rolling his eyes and sighing in exasperation.
Regardless of their quirks, Dean and Castiel are the best of friends.
Castiel: An Archangel. The one who killed me.
Dean: Excuse me?
Castiel: His name is Raphael.
Dean: You were wasted by a teenage mutant ninja angel?
"Read the bible. Angels are warriors of God. I'm a soldier." - to Dean in episode 4x02
"It's the archangel! I'll hold him off, I'll hold them ALL off! Just stop Sam!" - telling Dean to stop Sam from inadvertenly raising Lucifer in episode 4x22
"You are not taking Sam Winchesters. I won't let you." - to Lucifer in episode 5x10
"I'm not an angel anymore. I'm your new God. A better one. So you will bow down and profess your love unto me, your Lord... or I shall destroy you." - to Sam and Dean in episode 6x22
"You know, I've been here for a very long time. And I remember many things. I remember being at a shoreline. Watching a little gray fish heave itself up on the beach, and an older brother saying, 'Don't step on that fish, Castiel. Big plans for that fish.' I remember the Tower of Babel, all 37 feet of it, which I suppose was impressive at the time. And when it fell, they howled divine wrath. But come on, dried dung can only be stacked so high. I remember Cain and Abel. David and Goliath, Sodom and Gomorrah. And of course, I remember the most remarkable event - remarkable because it never came to pass. It was averted by two boys, an old drunk, and a fallen angel. The grand story. And we ripped up the ending, and the rules, and destiny, leaving nothing but freedom and choice." - narration at the start of episode 6x20
"You should show me some respect. I dragged you out of Hell. I can throw you back in." - to Dean in episode 4x03
"I don't understand...why do you want me to say my name?" - setting up his voicemail on his cell phone in episode 5x16
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