Unmanned aerial vehicles are rapidly gaining popularity in a variety of environmental monitoring tasks. A key requirement for their autonomous operation is the ability to perform efficient environmental mapping online, given limited onboard resources constraining operation time, travel distance, and computational capacity. To address this, we present an online adaptive-resolution approach for mapping terrain based on Gaussian Process fusion. A key aspect of our approach is an integral kernel encoding spatial correlation over the areas of grid cells, which enables modifying map resolution while maintaining correlations in a theoretically sound fashion. This way, we can retain details in areas of interest at higher map resolutions while compressing information in uninteresting areas at coarser resolutions to achieve a compact map representation of the environment. We evaluate the performance of our approach on both synthetic and real-world data. Results show that our method is more efficient in terms of mapping time and memory consumption without compromising on map quality. Finally, we integrate our mapping strategy into an adaptive path planning framework to show that it facilitates information gathering efficiency in online settings.