Let's take the Wikipedia page on Adiabatic quantum computation. The idea is pretty straightforward: you know there exists a quantum-mechanical system such that you can read the solution to your problem from its ground energy state. This is your target, from which you will be able to read a solution. You take some simple quantum-mechanical system which is already in its ground energy state and make "slow" adjustments to the external conditions of the system so that the simple system becomes the target system. If the modifications are slow enough, the system will stay in its ground state, and you can read your answer from it at the end of the process. To quote Wikipedia: "According to the adiabatic theorem, we start from the ground state of Hamiltonian H_B at beginning, go through an adiabatic process, and at last ending in the ground state of problem Hamiltonian H_P. Then we measure the z-component of each of the n spins in the final state, this will produce a string z_1,z_2,\dots,z_n which is highly likely to be the result of our satisfiability problem."
The correctness of the result is function of the speed at which we try to make the system change. Under some given speed, the error probability becomes tiny. I don't know how tiny though, perhaps it's a little bit higher than in electronic computers on Earth. Regardless, plenty of extremely important real-life applications can deal with that, like scheduling problems or anything where we use heuristics for instance.