List Survey Publicly: Means that the survey will appear in a list of available surveys if the user goes to your generic LimeSurvey URL (ie: "
www.yourdomain.com/limesurvey/"
Allow Public Registration: Means that in a token based survey (ie: a survey that you can only do if you have a token), those who turn up at the surveys URL (ie: "
www.yourdomain.com/limesurvey/index.php?sid=123456") who don't have a token will be offered the chance to register and receive a token
Setting "Allow Public Registration" to yes, will only have an effect if you enable tokens. It's a way of letting people in to a closed survey.
If you just want people to be able to connect to a URL, and fill out the survey (ie: really make it public), then you shouldn't enable tokens for the survey.