The location of this button varies based on the theme you use. You can find the button on the movie details screen most of the time.
The refresh button will trigger a metadata refresh. This is useful for scenarios where your metadata is retrieved from the builtin metadata providers and you want to check if there is more up-to-date information available online.
In case of local metadata, Media Browser will refresh the content from mymovies.xml. This is useful in cases the latest metadata is not reflected in Media Browser.
Note: As of version 2.3.0 (codename Draco) Media Browser will refresh the highlighted item AND all children. This means that, for example, if you highlight a Media Collection and refresh from there, all the the media inside that collection will be refreshed.
SubtitleProvider Plugin specific
If you use the SubtitleProvider plugin the refresh button also performs a check to see if there is a subtitle in the configured language available.
SubtitleProvider will then automatically download that subtitle file, extract and rename it accordingly.
More information on the subtitle plugin can be found here.