MathJax performs much of its activity asynchronously, meaning that the calls that you make to initiate these actions will return before the actions are completed, and your code will continue to run even though the actions have not been finished (and may not even be started yet). Actions such as loading files, loading web-based fonts, and creating stylesheets all happen asynchronously within the browser, and since JavaScript has no method of halting a program while waiting for an action to complete, synchronizing your code with these types of actions is made much more difficult. MathJax uses three mechanisms to overcome this language shortcoming: callbacks, queues, and signals.
Callbacks are functions that are called when an action is completed, so that your code can continue where it left off when the action was initiated. Rather than have a single routine that initiates an action, waits for it to complete, and then goes on, you break the function into two parts: a first part that sets up and initiates the action, and a second that runs after the action is finished. Callbacks are similar to event handlers that you attach to DOM elements, and are called when a certain action occurs. See the Callback Object reference page for details of how to specify a callback.
Queues are MathJax’s means of synchronizing actions that must be performed sequentially, even when they involve asynchronous events like loading files or dynamically creating stylesheets. The actions that you put in the queue are Callback objects that will be performed in sequence, with MathJax handling the linking of one action to the next. MathJax maintains a master queue that you can use to synchronize with MathJax, but you can also create your own private queues for actions that need to be synchronized with each other, but not to MathJax as a whole. See the Queue Object reference page for more details.
Signals are another means of synchronizing your own code with MathJax. Many of the important actions that MathJax takes (like typesetting new math on the page, or loading an external component) are “announced” by posting a message to a special object called a Signal. Your code can register an interest in receiving one or more of these signals by providing a callback to be called when the signal is posted. When the signal arrives, MathJax will call your code. This works somewhat like an event handler, except that many different types of events can go through the same signal, and the signals have a “memory”, meaning that if you register an interest in a particular type of signal and that signal has already occurred, you will be told about the past occurrences as well as any future ones. See the Signal Object reference page for more details. See also the test/sample-signals.html file in the MathJax test directory for a working example of using signals.
Each of these is explained in more detail in the links below: