That's the problem with the "americanisation" of english! Americans say check, we say tick. So when DannyG says "Now check the 'never dial a connection button", he means tick it - (or mark it in your words).
The reason this dialogue box is popping up is because a programme running on your PC wants to make a connection to the internet. If you don't have one at that time then because you have dial the default connection ticked, your PC is asking you if it is OK to make one. By ticking 'never dial a connection, you stop a programme from being able to make the call. The downside is that you will have to manually make a connection every time you want to use the internet and every time your connection is dropped.
You really should find out what is making these calls. Most probably it is an autoupdate feature of a background programme you have such as antivirus or realplayer. You should be able to turn this off from within the offending programme. More worryingly you may have a virus or trojan on your system. Make sure your virus definitions are current and do a scan.
Hope this helps.