As a smuggler in Star Wars, Han Solo regularly found himself in tight spots because things can easily go sideways when taking advantage of career criminals and crime syndicates. He was used to watching his back and was always aware of the past deals that could come back to haunt him or the goons that could be waiting for him around every corner. However, in The Empire Strikes Back, his past with Jabba the Hutt finally caught up with him, and he ended being frozen in carbonite. Later, he described the experience as absolutely awful.
As the name implies, carbon-freezing was the process of freezing liquid carbonite into a solid. It was a very old process that was originally used to preserve and protect goods during transportation. Also, legend has it that before hyperspace travel was possible, some travelers froze themselves in carbonite for long space journeys, but the extended freezing routinely resulted in hibernation or carbon sickness. As the years went on, the process was refined and became slightly more common.
Vader’s time on Cloud City was not his first experience with carbonite. When he was still Anakin Skywalker, he had himself frozen in the substance. Star Wars: The Clone Wars Season 3, Episode 18, “The Citadel,” showed how Anakin, Obi-Wan and their team froze themselves in carbonite to evade bio-scans en route to rescuing Jedi Master Even Piell from a Separatist Prison. The plan worked because being frozen had tricked the Separatists' life-detecting scanners. Since they were only frozen for a relatively short amount of time, they were able to quickly regain normal senses and bodily functions after unthawing, as if they had just been asleep.
In Star Wars #3, Leia was also briefly frozen in carbonite. When she, Luke and Lando returned to Cloud City to find Luke's blue lightsaber, they separated to carry out their different missions. While learning how to unthaw carbonite, Leia was captured by stormtroopers, and they froze her to transport her to an ISB outpost. Leia, however, was able to communicate with Luke through the Force, so he and Lando were able to free her. She, like Anakin in The Clone Wars, was only frozen for a brief amount of time, and was ready to fight when unthawed. Her experience shows that people are still at least semi-conscious while frozen in carbonite.
The last act of The Empire Strikes Back takes place on Cloud City where Han Solo was famously frozen in carbonite, but Han was only a guinea pig. Darth Vader knew that the facilities there were primitive, and that was why he wanted to test them before attempting to freeze Luke. Although Han was successfully frozen in the movie, there was soon trouble. Star Wars: War of the Bounty Hunters Alpha #1 shows that the carbonite matrix was unstable, and Boba Fett was forced to find someone to fix the technology so that Han didn't dissolve into goo.
When Han was finally unthawed in Return of the Jedi, the extended period of time being frozen, combined with the primitive freezing technology, caused him to have the classic symptoms of carbon sickness. Essentially, after being deprived of everything for months (six in Legends, 12 in canon), his body went into sensory overload. He was temporarily blind, dehydrated, weak, disorientated and he couldn’t remember what had happened to him.
The after-effects were bad enough, but the 1983 novelization of Return of the Jedi, which is no longer official canon, offered a glimpse into what it actually felt like for Han to be frozen. As the book explained, Han's time in the carbonite was like being in suspended animation – he was only alive enough to feel and know pain. It was described as, “a period that was, to him, timeless. It had been a grim sensation—as if for an eternity he’d been trying to draw breath, to move, to scream, every moment in conscious, painful asphyxiation.” Even though Han was not fully alive, the experience had been extremely gruesome. Without any senses, the time had felt like an eternity of constant agony. He couldn’t move, and he couldn’t satiate what he felt. He couldn’t even express himself with a scream because he was being suffocated. All he could do was subconsciously know that he was being held helplessly close to death.