data is the response you get back from the server. It depends on the dataType that you specify. If you specify json as the argument to the dataType parameter, jQuery will interpret the data received from the server as json.
textStatus gives you information about the response, as in whether it was successful, or if something bad happened. Possible values are:
success
error
notmodified
timeout
parsererror
If your success handler is called, then the value of textStatus is most likely success.
You will get a parsererror if the data is of an unexpected type. For example, if you specified that dataType is json, but the server returned XML, you will get a parsererror and your error handler will be called.