SSL certificate for moodle.org
When you, as an administrator, check for available updates or install an update, your Moodle site needs to communicate with moodle.org. This communication is done via the secure HTTPS protocol. Your Moodle site validates the SSL certificate of moodle.org (such as the Moodle plugins directory) and verifies its identity. To pass this verification, there must be a certificate (in the PEM format) of the certificate authority (CA) that issued the certificate for moodle.org installed on your server.
The SSL certificate for moodle.org has been issued by the DigiCert CA.
If this CA certificate is missing, the remote site (moodle.org) can not be verified and so your Moodle site will refuse to fetch the data (to protect you against so called man-in-the-middle attack). The exact location of the certificate on your server depends on the OS type and other settings. On Linux servers it may be typically found at /usr/share/ca-certificates/mozilla/DigiCert_High_Assurance_EV_Root_CA.crt for example.
A missing CA certificate results in an error when checking for available updates and attempting to install them.
Update your operating system (recommended)
The recommended way to fix this problem is to update your server's operating system so that it contains recent SSL certificates from common certificate authorities. This does not seem to help for Windows servers though. At Windows, the cURL library bundled with PHP does not use the CA certificates installed in the OS and you will have to use the alternative solution described below.
For Debian and RedHat based distributions, CA certificates are distributed in the ca-certificates package. Gentoo servers provide them via the app-misc/ca-certificates ebuild. It's also a good idea to make sure that the OpenSSL libraries (libssl) and cURL libraries (libcurl) are up-to-date on your server.
Provide the CA certificate manually
If updating the operating system is not an option for you, or the administrator of the server refuses to update the CA certificates on the server (despite there being no good reason for not doing so), or updating the CA installed in the OS did not help (such as in case of Windows servers), a possible workaround is to download the bundle of required certificates from the cURL site. You need to download the file cacert.pem from there and put it into your moodledata/moodleorgca.crt file (i.e. download the cacert.pem file, rename it to moodleorgca.crt and upload it into your mooodledata). If this file is found in moodledata, Moodle will use it instead of relying on certificates provided by the operating system.
It must be highlighted that having the CA certificate on your server's operating system as described above is really the recommended solution. The solution based on moodleorgca.crt should only be considered as a temporary fix (although it seems to be the only way to make it work at Windows servers).