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Endowed with higher levels of autonomy, robots are required to perform increasingly complex manipulation tasks. Learning from demonstration is arising as a promising paradigm for transferring skills to robots. It allows to implicitly learn task constraints from observing the motion executed by a human teacher, which can enable adaptive behavior. We present a novel Gaussian-Process-based learning from demonstration approach. This probabilistic representation allows to generalize over multiple demonstrations, and encode variability along the different phases of the task. In this paper, we address how Gaussian Processes can be used to effectively learn a policy from trajectories in task space. We also present a method to efficiently adapt the policy to fulfill new requirements, and to modulate the robot behavior as a function of task variability. This approach is illustrated through a real-world application using the TIAGo robot.