ng-mouseover and leave to toggle item using mouse in angularjs

Angular solution

You can fix it like this:

$scope.hoverIn = function(){
    this.hoverEdit = true;
};

$scope.hoverOut = function(){
    this.hoverEdit = false;
};

Inside of ngMouseover (and similar) functions context is a current item scope, so this refers to the current child scope.

Also you need to put ngRepeat on li:

<ul>
    <li ng-repeat="task in tasks" ng-mouseover="hoverIn()" ng-mouseleave="hoverOut()">
        {{task.name}}
        <span ng-show="hoverEdit">
            <a>Edit</a>
        </span>
    </li>
</ul>

Demo

CSS solution

However, when possible try to do such things with CSS only, this would be the optimal solution and no JS required:

ul li span {display: none;}
ul li:hover span {display: inline;}