Versions: SharePoint 2013
Definitions: SharePoint group, SharePoint user, SharePoint JavaScript API
References:
Tags: #JavaScript, #JQuery, #SharePoint
Example of function that gets the user’s most important group using SharePoint JavaScript API

/**
 * Returns the user's highest level group
 * @param {string[]} groups - Array of existings groups order by DESC
 * @returns {string} - User's group name
 */

function getUserGroup(userId, groups) 
{
	$.ajax({
		
		url: _spPageContextInfo.webAbsoluteUrl + "/_api/web/GetUserById("+ id +")/Groups?$select=Title",
		method: "GET",
		headers: { "Accept" : "application/json; odata=verbose" },
		success: function (data) {
				var items = data.d.results;
				for(var i=0; i < groups.length; i++) 
				{
					for(var j=0; j < items.length; j++)
					{
						if (items[j]['Title'] == groups[i])
						{ 
							return groups[i];						
						}
								
					}
				}
		},
		error: function (data) {
		}
	});
}