The idea behind a SSTO craft is that it can not just get to orbit in one piece, but also back to the ground, refuel and start again. That means after the initial investment of building the SSTO launch system, a launch only costs you the fuel (theoretically - practically you will always have some components which will need to be replaced more or less regularly).
With a multi-stage craft, the spent stages usually sink into the ocean, disintegrate in the atmosphere or end up in a graveyard orbit which means that they can only be used once and need to be rebuild from scratch. Each launch has the price-tag of building the whole launch system.
A middle-ground between both methods is a multi-stage launch system where the spent stages can be recovered, refueled and reused. This seems to combine the advantages of both methods - no wasted hardware and no dead weight into orbit. But it is technically a lot more complex to do. The Space Shuttle was the first launch-system which tried this. Its solid rocket boosters were recovered and refueled. Unfortunately the execution was flawed: Refilling the boosters with solid fuel was almost as expensive as rebuilding them.
A newer system which tries this is the reusable version of the Falcon 9. SpaceX is currently developing a lower stage which returns to the launch-site autonomously. The system uses liquid-fuel, which is a lot cheaper and a lot easier to get into the booster than solid-fuel. Also, because the stage returns to the launch-site on its own power, an expensive recovery-operation becomes unnecessary.
The downside compared to an expendable launch system is that the lower stage needs to conserve some of its fuel for returning and landing, which means less fuel for the payload. The downside compared to an SSTO is that each stage must be a full-fledged craft capable of autonomous navigation, maneuvering and landing which inevitably means that lots of systems will be redundant.