Beyond just restating the court's constitutional role as an arbiter of the constitution and one part of a system of checks and balances between the branches of government, I think the most important role the court has played over the last ~100 years is in progressively moving closer and closer to actually realizing some of the ideals found in the Declaration of Independence, e.g. in recognizing that the right to life, liberty, and the pursuit of happiness really ought to be a right enjoyed by all.
Expanding the actual protection of rights to more and more people has tended to involve defending the ideal against a hegemonic culture that has often rejected rights in practice for various groups, whether African Americans, women, LGBTQ people, and so on. The court has also played an important role in expanding individual liberty against various authoritarian impulses, especially with regard to the first amendment during the course of the 20th century.
I think the court also ought to play a role in defending the democratic process from being eroded in various ways, i.e. by strongly protecting voting rights and rejecting gerrymandering schemes, and taking a stronger interest in the corrupting influences of money on the process. I think the court has failed more often than not lately in that regard.
All of the above in my view relates directly to the court being a custodian of the spirit of the constitution (e.g. I find "originalist" presuppostions dubious, for a number of reasons) and that ideal which the Declaration so eloquently states.
