Great Expectations is a Victorian era book because, first, because it was published in the Victorian era—the era of Queen Victoria's reign, which lasted from 1837 to 1901. What you probably mean, however, is to ask what makes it a characteristic Victorian novel—and it has many Victorian traits. I will focus briefly on three: length, sentimentality, and society.
First, one of the notable qualities of the Victorian novel is its great length. This is because these novels were often serialized in journals, and Great Expectations was no exception to that rule. Week after week sales of a magazine would rise because people were interested in reading the next chapter in an ongoing story—and, of course, in the interests of profit, it made sense to lengthen a popular tale. Further, the chapters would later be gathered into a novel that, to make the most money, was released in a three-volume set. The length of Great Expectations therefore reflects the economic pressures of the times—and is typical of a Victorian novel.
Second, the Victorians believed emotion—sentiment—was an important way to move people's souls and change their behavior. Great Expectations is unabashedly sentimental in its portrayal of the goodhearted and loyal Joe, as well in the death of Magwitch—the Victorians loved a good deathbed scene, and Dickens does not disappoint.
Finally, the novel is Victorian in reflecting the society of its time, in which social class is all important. Key to this novel is the idea of working class boy rising to become a gentleman and what those class distinctions mean in a society of haves and (mostly) have-nots.