Initially the SDN concept relied on a single controller but this was heavily criticized for introducing a single point of failure. If your controller's compute hardware died or the network was partitioned preventing contact with switches, in effect you lose the ability to adapt to network changes.
Logically centralized refers to resolving this problem with many controllers that are widely physically distributed, to provide fail-over redundancy and guard against network partitioning. For example, when considering controller placement you will examine the likelihood of natural disasters (eg. earthquake, tsunami) and look to ensure you have controllers in regions that are unlikely to all be hit by the same event.
Logically centralized also refers to the idea that these distributed controllers act as a single controller from the perspective of the Network Operator running the system. In practice, while solving the big problems, distributed controllers introduce new issues related now being a distributed database for network rules.