Maker ID is a 7-character, unique signature of a maker/studio. It's short enough to squeeze it into your profile description or on the fursuitter badge, but whoever sees it can just look it up here and will find your creator.
For example, imagine someone posted a nice photo of himself goofing around in his fursuit. You navigate to the guy's profile:
Among all the insignificant information he provided you see what you're looking for: who created his fursuit. The scissors symbol is optional, you'd know the ID by its specific format anyway.
Having a known maker ID you can easily find them on the list using the search field on the right:
You can find the maker ID of a studio in the top-left corner of the details pop-up:
In fact, this is a link you can copy and paste. It leads directly to your maker's info.
If a maker's ID does not show up, it means they didn't update their data in a long time. How about you poke them, so they send the updates?