Data repositories allow researchers to deposit research outputs in a way that makes them available for other researchers to use. You can use Re3 to search for repositoires in a suject area, while Google dataset search lets you search across repositories and the web for datasets.
There are a large number of repositories - ranging from multi-disciplinary ones (like those linked to below) to more targeted subject specific respoitories. In addition there are governmental and organisational respoitories that collect data produced by those bodies.