Display custom module output in a panel pane

there's several options :

let's say you have a function mymodule_generate_table() :

1- add a "New custom content" pane to your panel, choose the PHP code input format, and call mymodule_generate_table() from there
2- create a block in your module, set $block['content']=mymodule_generate_table(), and add this new block to your panel
3- create a basic block in your module with $block['content'] set to anything (not empty), and do what you want in the template file block-mymodule-delta.tpl.php

the 3rd method, gives total control over visibility and theming, and avoids storing code into the database
you can set $block['myparam'] inside your module and use it as $block->myparams inside your template
you can set $block['content']='' inside your module to hide the block

souk's advice is a little misleading. You 'can' do all of those things, but none of them are going to provide you the greatest amount of flexibility.

I'd _strongly_ advise against #1. The custom content pane really isn't designed for anything systemic, it's designed for quick-fix, single-use hack jobs, basically.

#2 is a back way in to panels that will work, but again, with a pretty limited amount of flexibility. Of the three, it's the most advisable.

#3 essentially just dodges Panels entirely, and while you might want to use something like it eventually, it's really at the end of the line.

If you're looking to build something stable and flexible, then write a panels content type plugin. Now since you're new to drupal (and asking you to do that is a bit like asking you to jump in the deep, DEEP end of the pool), #2 might be your best bet for now. But with content type plugins, you've at least got a really detailed guide about all the different things you can do with it: http://doxy.samboyer.org/panels2/panels_api_plugins_content_types.html