We've talked about Christminster in our "Character Analysis" of Jude (check under the heading "Christminster: The Crazed Self-Destruction Continues"), but we want to talk about the city itself in a little more detail here.
Christminster is, at various times, referred to as 'the city of light' (1.3.42) and the 'New Jerusalem' (1.3.19), meaning that it is both (a) beautiful, (b) a symbol for a hopeful future, and (c) a place of huge spiritual significance.
For Jude specifically, the city symbolizes not only knowledge, learning, and purity, but also his desire for a new life. After all, Jude grows up in a small town where his choices for the future are extremely limited. Think about his jobs along the way, before he makes the big move to the big city: he is an official, employed bird scarer (seriously—he's a living scarecrow); he works for his aunt the baker, and he picks up stonemasonry. These are all fine jobs (well, except maybe the scarecrow one), but not necessarily ideal for a young man who prizes learning above all else.
As Jude dreams of Christminster and of the example Phillotson set for him by going there to become a scholar, Jude sees the chance at an entirely new kind of life, with opportunities to distinguish himself as something other than a champion bird frightener. He believes that, if he can get to the city, he will be able to shake off his rural roots and pursue learning to its fullest. Christminster will allow Jude a spiritual (and professional) rebirth.
Unfortunately, the difference between Jude's dream of Christminster and the real thing quickly becomes apparent. And Jude's unchanging pursuit of his dream of Christminster leads to Jude's destruction. To sum up the difference between Jude's fake Christminster and what we actually see in the novel, we have the narrator's brilliant comment: 'What at night had been perfect and ideal was by day the more or less defective real' (2.2.4).
That line sets the tone for Christminster's later significance in the novel. Where, for Jude, the city represents hope, opportunity, and professional achievement, we later see the city as a symbol for Jude's failed hopes and dreams. Christminster's "defective real" quality by day indicates the falseness of the promise that the city offers to Jude long before Jude realizes that he will never truly be a part of Christminster culture. Indeed, Jude only speaks about his failure to join Christminster in Part Sixth: 'My failure is reflected on me by every one of those young fellows' (6.1.9). Continuing on, Jude comments later, 'It takes two or three generations to do what I tried to do in one" (6.1.32).
Jude is clearly a smart guy who is more than talented enough to go to Christminster. What keeps him out of the university is social convention and prejudice. When Jude looks at the young people getting their degrees, he feels envious. But he also recognizes that his ambition was too much for the people of his time: it will take "two or three generations" for attitudes to change enough for working class students to break into the university establishment, whereas Jude hoped and dreamed (as he has a right to!) that he could find a place for himself right off the bat.
Jude the Obscure strongly emphasizes Jude's intelligence, drive, and ambition. And it also strongly emphasizes the social forces that unfairly keep Jude out of the university and out of Christminster. As the physical symbol of the wealth and privilege that Jude seeks and fails to get, Christminster stands in for that larger, messed-up world that completely rejects Jude for daring to find ambition and hope while coming from the wrong side of the tracks.