The search filter is a small drop down search form that appears on the browse page for searching within the category/folder you are browsing. It expands by clicking the 'more' down arrow.
The attributes that appear on this filter (in addition to the always shown keyword box) are configured using the 'Search results filter' display attribute group. To change the selected attributes go to Admin > Attributes > Display Attributes > Searching > Search results filter and add, remove or reorder attributes in the list.
Only date, text, dropdown list, option list and check list attributes are valid for display on the search results filter.