Answers suggesting to disable CURLOPT_SSL_VERIFYPEER
should not be accepted. The question is "Why doesn't it work with cURL", and as correctly pointed out by Martijn Hols, it is dangerous.
The error is probably caused by not having an up-to-date bundle of CA root certificates. This is typically a text file with a bunch of cryptographic signatures that curl uses to verify a host’s SSL certificate.
You need to make sure that your installation of PHP has one of these files, and that it’s up to date (otherwise download one here: http://curl.haxx.se/docs/caextract.html).
Then set in php.ini:
curl.cainfo = <absolute_path_to> cacert.pem
If you are setting it at runtime, use:
curl_setopt ($ch, CURLOPT_CAINFO, dirname(__FILE__)."/cacert.pem");