At liftoff the first stage is responsible for accelerating the vehicle. At some point the second stage detaches from the first stage and continues to orbit under its own power.
The advantage of such a system is that the entire mass of the spacecraft is not carried into orbit. This reduces the difficulty involved in reaching orbital velocity.
It is not always clear when a vehicle is a DSTO. Many designs which use a very small boost at the beginning of their flight are referred to as single-stage-to-orbit. Some have also coined the expression 1.5STO for 'one-and-a-half-stage-to-orbit', e.g., the Atlas. Also, many launch vehicles have side-mounted booster rockets which are jettisoned early which are called "stage-0".
With reference to a reusable launch system this approach is often proposed as an alternative to single-stage-to-orbit (or SSTO). Its supporters argue that, since each stage may have a lower mass ratio than an SSTO launch system, such a system may be built without approaching as close to the limitations of its structural materials. It therefore should require less maintenance, less testing, experience fewer failures and have a longer working life.
Critics argue that the increased complexity of designing two separate stages that must interact, the logistics involved in returning the first stage to the launch site, and the difficulties of conducting incremental testing on a second stage will outweigh these benefits. In the case of airplane-like lower stages they also argue how difficult high speed aircraft (like the SR-71) are to develop and operate, and question performance claims. Many 'mini-shuttle' designs that use transport aircraft as first stages also face similar problems with ice/foam as the Space Shuttle due to the requirement they also carry a large external tank for their fuel.
On the other hand, the two-stage approach allows the lower stage to be optimized for operation in the Earth's lower atmosphere, where pressure and drag are high, while the upper stage can be optimized for operation in the near-vacuum conditions of the later part of the launch. This allows an increase in the payload mass fraction of a two-stage vehicle over single-stage or stage-and-a-half vehicles, which have to perform in both environments using the same hardware.
Many TSTO designs comprise an airplane-like first stage and a rocket-like second stage. The airplane elements can be wings, air-breathing engines, or both. This approach appeals because it transforms Earth's atmosphere from an obstacle into an advantage. Above a certain speed and altitude, wings and scramjets cease being effective, and the rocket is deployed to complete the trip to orbit.