In this paper, we address the problem of adaptive path planning for accurate semantic segmentation of terrain using unmanned aerial vehicles (UAVs). The usage of UAVs for terrain monitoring and remote sensing is rapidly gaining momentum due to their high mobility, low cost, and flexible deployment. However, a key challenge is planning missions to maximize the value of acquired data in large environments given flight time limitations. To address this, we propose an online planning algorithm which adapts the UAV paths to obtain high- resolution semantic segmentations necessary in areas on the terrain with fine details as they are detected in incoming images. This enables us to perform close inspections at low altitudes only where required, without wasting energy on exhaustive mapping at maximum resolution. A key feature of our approach is a new accuracy model for deep learning-based architectures that captures the relationship between UAV altitude and semantic segmentation accuracy. We evaluate our approach on the application of crop/weed segmentation in precision agriculture using real-world field data.