var appweburl = "http://SharePointsiteUrl";
var scriptbase = appweburl + "/_layouts/15/";
$.getScript(scriptbase + "SP.RequestExecutor.js", execCrossDomainRequest);

function execCrossDomainRequest() {
   var executor = new SP.RequestExecutor(appweburl);

   executor.executeAsync(
        {
            url:
                appweburl +
                "/_api/web/lists/getbytitle('Listname')/items",
            method: "GET",
            headers: { "Accept": "application/json; odata=verbose" },
            success: successHandler,
            error: errorHandler
        }
    );

}