Good first answer chronologically, https://space.stackexchange.com/a/63586/51373 Please allow me to expand on that, as there is a little more to it.
The pump draws the liquid into it's "eye" by creating a low pressure area as described in that link. The fluid then enters the spinning impeller region. At this point it's velocity is increased by the spinning vanes moving it along, accelerating the fluid; the energy it takes to do this is provided by the motor or engine that's driving the shaft. As it moves outwards along the impeller, the distance covered gets larger and larger, so the fluid is sped up dramatically more and more as it nears the outer edges of the vanes.
Finally, the water exits the vanes into what is called the Volute, which gradually gets larger to accommodate all the fluid exiting the vanes, and leads to the outlet. As it gets larger just before the exit, the fluid slows dramatically. The energy from it's velocity is converted into raising pressure, since energy can neither be created nor destroyed, but merely transferred to another form. Hence, even though the inlet and outlet flows are the same, the pressure has been raised on the outlet.
High pressure pumps may have multiple "stages" where this action is repeated a number of times; the outlet of the first stage is directed into the second stage inlet, and that continues in series for all of the stages present. Each stage boosts the pressure higher than before. From a manufacturing standpoint, to maintain simplicity, most of the time all of the impellers are driven by the same shaft, and internal passages carry the flow from one stage outlet to the next stage inlet.
As far as I know, most applications for rocket turbopumps are single stage.
So in summary, a centrifugal pump raises the pressure of a fluid by mechanically imparting energy into the fluid by raising it's velocity, and then at the exit that velocity energy is changed into a raised pressure energy.
Edit: I've seen large steam turbine-driven pumps that could raise pressure by up to 800 psi in a single stage. I'd imagine that these particular pumps are capable of much higher pressures, since you would have to exceed chamber pressure to get flow in there; a Raptor chamber runs at about 30MPa (4,400 psi), plus whatever is needed to push that much fuel and oxidizer through the injector plate.
Extra info that may be of help:
The discharge pressure of a pump varies depending on the resistance to flow in the downstream system. In a more restrictive system, flow is lower, and pressure rises.
At the extreme where the discharge is closed completely, the pump will reach it's maximum output pressure; and as there is no flow or acceleration of the fluid, the energy required drops to a minimum. If a motor is driving the pump, for instance, it's current will be very low. This is called deadheading a pump, and is bad for various reasons; chief among them is that the impeller is still spinning, but with no flow that minimum energy ends up heating the water stuck in the pump, and the temperature just keeps going up. The fluid could start to flash into steam (pumping a water/vapor mixture causes extreme vibration) or the high temperatures could cause numerous other malfunctions.
At the other extreme, where the discharge is essentially wide open and offering little resistance, output pressure will drop significantly, but since we are moving a lot of mass, the energy requirement goes way up. This is called runout. The main issue here is that the pressure at the eye may go so low because of restrictions in the supply line that the fluid starts to boil, forming very small bubbles. As those bubbles move through the pump and pressure increases, they collapse violently, which poses a tremendous local shock on the impeller, actually leading to pitting of the impeller surface and eventual failure. That process is called cavitation.
So a centrifugal pump has to operate in a specific range. Deadheading and runout are both potential causes of pump failure.
Reference: Here's a link that provides a good explanation, thank you Organic Marble for the suggestion.