Two big questions drive the mission. The first is dark energy, the name given to whatever is causing the expansion of the universe to accelerate. Roman will survey something on the order of a billion galaxies, measuring how they are distributed and subtly distorted, to trace how that expansion has changed across the history of the universe. It is not designed to explain dark energy so much as to measure its effects far more precisely than we can now.
The second is planets. Roman will stare at the crowded star fields toward the centre of our galaxy and watch for gravitational microlensing, the brief brightening that happens when one star, and any planets around it, passes in front of another and bends its light. Monitoring something like 200 million stars, it is expected to find well over a thousand planets this way, including cold, distant worlds far from their stars that other techniques tend to miss.
But have patience: “After the 30 August launch, Roman faces the same outbound trip as Webb did, out to the second Lagrange point about 1.5 million kilometres from Earth, followed by months of commissioning before any science begins in earnest.”