TequillaMockingBird and nocake have given informative answers (thanks!), but I thought I'd chip in to help put people at ease.
The content on this site is related to something called a cryptographic hash function. The sequence of letters on the left are the result of entering the corresponding text on the right hand side into one of a class of algorithms, consisting of MD5 among many others. There are several websites like the one linked to which provide reverse-lookup tables (called rainbow tables) for cryptographic hashes of corresponding input text, for various reasons. This particular one is part of a reverse lookup table for a MySQL hashing algorithms.
Put simply, people use lists like this to find, given a sequence of characters like "c5010012cec4620048adb4b2ed9574e9", the sequence of characters "ireenmvi", as long as they know the algorithm being used.
The fact that this site might list your nickname doesn't mean your password has been exposed or that any other information about your account is at risk, as the information by itself is not enough to do anything. Your computer details haven't been crawled. Since anyone can find Mumsnet nicknames by browsing Talk, as has been said, I would guess someone has just entered a bunch of text that they've found online (intentionally using Mumsnet nicknames or not), and the entries have been added to their database.
@nocake
That website simply shows what an MD5 encrypted version of each of those username looks like (I'm assuming it's MD5 because that's what it looks like). It is unlikely to help anyone hack a computer system because most of them encrypted the username and password together, rather than just the username.
You're more or less right, nocake, though the algorithm isn't MD5. The URL has a give-away to the one used: "mysql". :)
Anyone interested in reading more about this stuff can check Wikipedia's articles on Cryptographic hash functions, and rainbow tables.