A data repository is simply a place to store data. Using a repository to store and preserve your data versus hosting it on your website facilitates its discovery and preservation. This will ensure the data is accessible to other researchers and that care will be taken to preserve the data over time.
Many options exist for storage and accessibility of research data. If you're looking for a place to host your data, consider whether you want the data to be shared publicly or accessible only to you and a select group. These decisions will help to guide the proper data repository for your data. There may be more than one solution that works to address questions of accessibility and long-term storage of your research.
If you are a current UCL staff or research student, there is a free option available: UCL's institutional Research Data Repository can host data and make it freely available on the Web.
This is not an exhaustive list! Use a service such as R3data to find repositories geared to your subject area.
Instead of archiving research data in a data repository, you may choose to publish an article about your data collection. This is not necessarily common for all disciplines. Some examples of data journals where you can publish your data and dataset, are: