It means something related to the works of Charles Dickens, but is usually used to refer to depressing circumstances, as Dickens often told stories of the poor of Victorian England.
From The Free Dictionary:
Of, relating to, or reminiscent of the works of Charles Dickens, especially with regard to […] grim depictions of the plight of children and the urban poor.
From The Cambridge Dictionary:
relating to or similar to something described in the books of Charles Dickens, especially living or working conditions that are below an acceptable standard:
Why I Looked It Up
Reading a book on science history, one scientist’s life was depicted in a sad retrospective, at one point being said to “reach its Dickensian nadir.”