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We consider an edge computing framework for online distributed learning in UAV swarm, which allows swarm to collect data and train machine learning (ML) models over the air. Usually, UAVs are used as sensors to collect and transmit data to ground for further processing. However, the overhead for raw data transmission are becoming unaffordable as the task gets complex and the timeliness gets increasingly rigorous. Therefore, We have proposed a new distributed online learning scheme to allow each UAV collect data locally as well as perform ML model training onboard. We have theoretically proved the convergence of the ML model to be trained, and the performance gap between central training method and proposed scheme is analyzed. Furthermore, we have bridged the sensing and transmission via the definition of importance of each UAV based on its contribution in training, where we extend the widely-used timeliness metric Age of Information (AoI) to Age of Updates (AoU), and thus the data freshness and data value in training process are combined together. The performance of the proposed distributed learning scheme is validated, and the difference between AoI and AoU are compared via simulations.