In jQuery, AJAX requests can fail for various reasons, such as a network error, a server error, or an invalid response from the server. To handle these errors, you can use the `error` callback function in the AJAX request.

The `error` function is executed if the request fails, and it receives three parameters: `jqXHR` (the XMLHttpRequest object), `textStatus` (a string that describes the type of error that occurred), and `errorThrown` (an optional exception object, if one occurred).

Here's an example of how to handle errors in a jQuery AJAX request:

$.ajax({
 url: 'https://example.com/api/data',
 method: 'GET',
 dataType: 'json',
 success: function(data) {
   // Handle successful response here
 },
 error: function(jqXHR, textStatus, errorThrown) {
   console.log('AJAX request failed: ' + textStatus + ', ' + errorThrown);
   // Handle error here
 }
});

In the `error` function, you can perform any necessary error handling, such as displaying an error message to the user, logging the error to a server, or retrying the request.

It's also worth noting that you can use the `fail` method to attach a function to the deferred object returned by `$.ajax()`. This allows you to handle errors in a more elegant and concise way, as shown in the following example:

$.ajax({
 url: 'https://example.com/api/data',
 method: 'GET',
 dataType: 'json'
})
.done(function(data) {
 // Handle successful response here
})
.fail(function(jqXHR, textStatus, errorThrown) {
 console.log('AJAX request failed: ' + textStatus + ', ' + errorThrown);
 // Handle error here
});

In this case, the `done` function is executed if the request is successful, and the `fail` function is executed if the request fails.