24 connect is for sending and receiving wii-mail, letting your mii travel and to download news/weather reports. It will give you notices that you can update your software if the update involves the addition of a new channel such as the opinion or news channel.
To be an effective e-mail client it really does need to be connected 24 hours or your mail will be delayed. I've found that the timed delay from me sending and e-mail from my main server to when it's received and posted by the wii to be in the range of 5 minutes or less (of course, that may increase as more and more people use the 24connect and start to tie up server/bandwidth).
I'm glad that it gives you the option of updating the software instead of just doing it automatically. Can you imagine the trouble that might occur if you turn off your router at night and it was in the middle of a download/update? You might just end up with a 'bricked' unit.