One way quantum computation (1WQC) uses an initially highly entangled state (called a cluster state), and then a pattern of single qubit measurements along different directions, together with feed-forward based on the results, in order to drive a quantum computation. The final result of the computation is obtained by measuring the last remaining qubits in the computational basis. 1WQC was introduced by Raussendorf and Briegl in 2001 [1]. The key feature is that the computation is not reversible since measurement "collapses" the state of the measured qubit, effectively disentangling it from the rest of the cluster. The essential concept underlying 1WQC is teleportation of quantum gates, extending the idea behind linear optical QC.
The main advantage of 1WQC is that it allows scalable universal QC in systems which have a probabilistic entangling procedure and single qubit measurements, but without a direct two-qubit interaction suitable for implementing deterministic entangling gates.
[1] A One-Way Quantum Computer, Robert Raussendorf and Hans J. Briegel, Phys. Rev. Lett. 86, 5188–5191 (2001)