cURL fetches content from a given URL. This may be text like a web page's HTML, or streamed binary files like images or zip archives. In the case of downloading some files, the URL given is actually a redirect to some other location. For example, the download for the MODX zip archive is redirected to the Amazon repository where the MODX files are stored. In other cases, images and other site files may actually be served from a CDN like CloudFlare.
The cURL option FOLLOWLOCATION will attempt to follow such redirects, but as the warning message states, PHP will not allow this if open_basedir is set in the PHP configuration.
If the site appears to still be functioning as expected, this is probably because a fallback has been coded into the application using the cURL request. If the FOLLOWLOCATION fails, a different method is used to get the file from the second, real, location. But the attempt was made, triggering that PHP warning. In such a case, it's annoying, but not fatal.
If the site is actually breaking, the files are not being fetched at all, then it's a bigger problem. There are three possible solutions. Get the sotfware trying to fetch the file fixed to have a fallback to work around the problem, have the PHP configuration modified to disable open_basedir, or move to a hosting provider that your site can work on.
If you like, there is some good discussion here
http://stackoverflow.com/questions/6918623/curlopt-followlocation-cannot-be-activated
[ed. note: sottwell last edited this post 10 years, 10 months ago.]