What is the Convention badge and why is it required to have for nomination in the moderator election?
Look here for a proper description of all the badges (including convention).
The convention badge requires that you have 10 posts in meta with a score of at least 2 each.
The reason that this would be required for nomination/election, I suspect, is that it is an indicator of:
Those indicators can be used somewhat accurately to determine whether you will be a good moderator.
But if you are active on meta, it is very likely that you are well integrated into the behavior of SO - a necessity for a good mod.
Thus, if you have made enough posts that have been upvoted enough on meta, that would be an indicator that you are "mod-worthy"
There was a good bit of discussion around this when the badges were originally put into place, and it's worth reading some of the commentary there (see also this question about the specifics of the badge). In general, badge requirements were added because many people had nominated themselves for the position of moderator who weren't prepared for the job or didn't fully realize what it entailed. The badges were meant as a way to filter for people who had been involved with the community in the same fashion that you'd expect in an active moderator.
The convention badge (having at least ten posts on a site's Meta upvoted a minimum of two times) indicates that someone has been at least somewhat active on the Meta site for a place on the Stack Exchange network.
This is very important for a moderator, because not only is Meta the place where policies are hashed out or announced, it is also the location where moderation-related actions are examined. If a moderator takes an unclear or unpopular action, odds are that someone will call them out on it here. We need to regularly check in on Meta so that we can explain why we might have done something, or to correct a mistake we might have made.
Additionally, people come to Meta for support, and those who are patient and helpful when answering questions of that type show the kinds of qualities that we look for in a moderator.