Federated Learning (FL) has shown great potential as a privacy-preserving solution to learning from decentralized data that are only accessible to end devices (i.e., clients). In many scenarios, however, a large proportion of the clients are probably in possession of low-quality data that are biased, noisy or even irrelevant. As a result, they could significantly slow down the convergence of the global model we aim to build and also compromise its quality. In light of this, we propose FedProf, a novel algorithm for optimizing FL under such circumstances without breaching data privacy. The key of our approach is a distributional representation profiling and matching scheme that uses the global model to dynamically profile data representations and allows for low-cost, lightweight representation matching. Based on the scheme we adaptively score each client and adjust its participation probability so as to mitigate the impact of low-value clients on the training process. We have conducted extensive experiments on public datasets using various FL settings. The results show that the selective behaviour of our algorithm leads to a significant reduction in the number of communication rounds and the amount of time (up to 2.4x speedup) for the global model to converge and also provides accuracy gain.