Mapping has two main purposes: grabbing properties from an array of items, and converting each item into something else.
Suppose you have an array of objects representing users:
var users = [
{ id: 1, name: "RedWolves" },
{ id: 2, name: "Ron DeVera" },
{ id: 3, name: "Jon Skeet" }
];
Mapping is a convenient way to grab a certain property from each item. For instance, you can convert it into an array of user IDs:
var userIds = $.map(users, function(u) { return u.id; });
As another example, say you have a collection of elements:
var ths = $('table tr th');
If you want to store the contents of those table headers for later use, you can get an array of their HTML contents:
var contents = $.map(ths, function(th) { return th.html(); });