Dead simple - whereas the standard AngularJS filter filter will return a match if the search string appears anywhere within the test string, this filter only returns a match if the test string starts with the search string.
For example:
// in your controller
$scope.things = ['cathode', 'house', 'chomp'];
$scope.search = "ho";// in your template
<li ng-repeat="thing in things | filter: search">{{thing}}</li> // cathode, house, chomp
<li ng-repeat="thing in things | startsWith: search">{{thing}}</li> // house