For the site-specific Meta, participation indicates a lot of important qualities of the nominee. The most important of these is that it presents an interest in the foundation of the site, not merely the functional front-end of the Q&A. Meta is where all the administration happens - participation indicates not only that you take a part in this administration, but that you read up on it and learn about it. Not just for discussions on existing issues, Meta activity also helps keep tabs on new developments that are announced. Knowing the background behind the rules is important in being able to properly enforce them.
Also, not all moderation is settled by simply closing or locking or protecting. Part of being a community run site is all the discussion on Meta. Disputes on rulings make some part of it, but there's also tagging conventions, retag requests, on-topic definitions, and general support issues. These are all good things to be a part of that help shape the community. Not required, but pretty helpful nonetheless.
Activity on Meta Stack Overflow helps in understanding a lot of the general engine, as well as keeping up on network-wide updates and news. But I personally find that it's mostly worthless without an ample backing of participation on the site-specific Meta. Background on Meta Stack Overflow may help understand the general case of what is on-topic and such, but it will not tell you how a specific community behaves. This is enough to do pretty well on the parent Q&A with asking, answering, and basic maintenance. But for representing the community as a moderator, you really need to have background in the community itself.