Content you purchase from the iTunes store can be authorised for up to five computers. That means five computers can be authorised for use with your iTunes purchases (which can be up to five of your own computers and possibly devices they are transferred to such as an iPod, or five including some other people's computers though that would be a bit naughty). I'm not sure if an iPod you transfer content to counts as an additional machine, but it probably does (can somebody help me with this as I do not know if each iPod that iTunes syncs with counts as an additional authorisation).
If you buy a new computer (or make a major upgrade with an existing one), you should first de-authorise that computer before from within iTunes to remove it from the count of machines your purchases are valid for. After the upgrade, log in and authorise it again and you will be fine.
I didn't do that when I replaced the hard-drive in my main box meaning it is using two authorisations, but that isn't a problem. If you reach the limit of five authorisations and need to install another because you have multiple old installations no longer usable, iTunes will offer a special option to de-authorise all machines (but will only allow you to do this once per year). That way you can remove all old machines or upgraded boxes you forgot to de-authorise from your limit of five in total, then re-authorise those you are using. That option will not be offered again for a year even if you hit the five limit in order to prevent it being abused to allow playback on many more than five computers.