Dickens was very committed so all sorts of social causes in his life. One of these was cleaning up some of London's most horrible slums and financing housing projects for the poor. Of course, this was before there were housing projects, before anyone knew what they would eventually turn into. At the time it seemed like a good, progressive idea.
Lots of characters in the novel are based on real-life people: Hortense was based on Marie Manning, a Swiss maid to fancy people who was convicted and hanged for murder a few years before the novel was written. Dickens attended the hanging and wrote about it for Household Words magazine.
Mrs. Jellyby is a pretty vicious portrait of Caroline Chisolm, a humanitarian who helped provide for women who had settled in Australia and India. She established schools and generally improved their lives, and for that her prize was... being made fun of in this book. Well, she's also about to become a saint in the Anglican Church, which is nice.
Skimpole is meant to skewer the writer Leigh Hunt. Dickens was totally psyched about how true-to-life this portrait of Hunt was and was really proud of the fact that everyone who knew Hunt recognized him in it. Still, it's a pretty mean portrayal, and it caused a scandal. To try to smooth things over, G. K. Chesterton (another writer) commented that Dickens "may never once have had the unfriendly thought, 'Suppose Hunt behaved like a rascal!'; he may have only had the fanciful thought, 'Suppose a rascal behaved like Hunt!'" Whatever. Either way, it's kind of cruel.
Boythorn was based on the writer Walter Savage Landor. He's not very widely read anymore, but he wrote some really cool imaginary dialogues between famous historical figures, fictional characters, and made-up people.
Bucket was also a real guy: Charles Frederick Field, one of the first detectives at the recently formed Scotland Yard. Dickens was so fascinated by what the cops did (which was a totally new thing at the time) that he would sometimes go on ride-alongs with them.
The case of Jarndyce and Jarndyce was a take-off of a real life Chancery case that lasted for 40 years.