I'm not a mod, but I am kind of biased, since I like all of our mods (I'm pretty sure all the ones I voted for were elected).
Personally, I find the bio section of a Stack Exchange profile to be one of the least interesting and informative parts of a user profile. If you want to learn about a mod (or any user), their activities will tell you much more than they could fit in a bio.
Right off the bat, looking at their network reputations tells you a lot. You can guess what kind of job they most likely have (it may not be their top rep, but likely in the top five), and you can quickly get a sense of how active they are on Stack Exchange in general.
If you're curious about knowledge, check out "all answers". The highest and lowest voted answers are often the most interesting. Looking at their questions also tells you a lot about what they don't know and some about what they do know. Looking at top voted questions from any user is a good way to pick up tips on how to ask good questions.
If you're more curious about someone's personality, I think that comes through more in comments. For instance, I suspect five to ten minutes perusing my comments will correctly suggest I'm an uptight know-it-all. It's not as obvious how to get there, though. Click on either all question or all answers, then all actions, then comments.
Finally, regarding mods in particular, they were all elected. During the election process, there are "campaigns" of a sort, including statements from the mods about why they think they should be mods and mod answers to user questions. Right now there's a related question listed for this question which is 2015 Moderator Election Q&A - Questionnaire, which is one meta post that will give you plenty of info about our mods in particular.
Looking at the activities, and particularly the comments (which are often left by our best users when there is a problem or down vote) was pretty much how I chose who to vote for in the mod election. People's comments tell you about how they view Stack Exchange and their fellow users. What more would you really want to know? (Ok, maybe the name of Dr. Mayhem's band so you can check out some YouTube videos).