If you have a brand-new Joomla installation that will be a big help in following along
Brand-New Joomla Site
If you have a brand new Joomla site installed, browse around and look at the URLs. For example, click on "Joomla Overview".
Joomla Overview URL
You'll notice the URL ends with Itemid=27. Try clicking on the next link down under "Main Menu". It should be called "Joomla License".
Joomla License URL
This time you'll notice the URL ends in Itemid=27. Try this on other pages and you'll see that each page is going to have a different Itemid at the end. The one you might be able to the see is the frontpage - the Itemd for that is always 1.
Where Else Can You See Itemids
Inside each menu there will be a column on the right-hand side listing Itemids
So What Do Itemids Do?
So we come to the key question .... notice on the frontpage, with an Itemid of 1, that there are lots of modules on the left, top and right. Now click on "Joomla License" which has an Itemid of 2:
Lots of those modules have vanished. However, let's just change the Itemid from 2 to 1:
And after doing that you'll see that all the frontpage modules have re-appeared. The Itemid controls which modules (and which templates) appear on a particular page:
Try going around the rest of your site and changing the Itemids on the URLs. See how the modules shift around. This is how Joomla controls which modules and templates appear on some pages but not others. If you have a problem with the modules appearing or not appearing where they should, it's very likely to be an Itemid issue.