Research sponsors and research institutions expect data to be handled responsibly in the interests of good academic practice. As the world becomes increasingly digitalized, this often includes an expectation to make research data publicly available in order to ensure greater transparency and to enable others to reuse the data. Publishing data benefits researchers' reputation and visibility in the academic community.
Provided there are no ethical or legal obstacles, research data can be published in subject-specific or interdisciplinary, institutional repositories or in special data journals. To enable others to reuse the data, they must be given a persistent identifier (e.g. DOI) and a license (e.g. Creative Commons) when published. We'll happily advise you on this.