Assuming you're calling a subroutine from MainLoop (the Tk event loop).

In order to keep the MainWindow up to date and provide user interaction while the subroutine is running, you need to use $mw->update or $mw->idletask.

Quotes from Tk::Widget:

$widget->update

One of two methods which are used to bring the application "up to date" by entering the event loop repeated until all pending events (including idle callbacks) have been processed.

The update method is useful in scripts where you are performing a long-running computation but you still want the application to respond to events such as user interactions; if you occasionally call update then user input will be processed during the next call to update.

$widget->idletasks

One of two methods which are used to bring the application "up to date" by entering the event loop repeated until all pending events (including idle callbacks) have been processed.

If the idletasks method is specified, then no new events or errors are processed; only idle callbacks are invoked. This causes operations that are normally deferred, such as display updates and window layout calculations, to be performed immediately.

The idletasks command is useful in scripts where changes have been made to the application's state and you want those changes to appear on the display immediately, rather than waiting for the script to complete. Most display updates are performed as idle callbacks, so idletasks will cause them to run. However, there are some kinds of updates that only happen in response to events, such as those triggered by window size changes; these updates will not occur in idletasks.