Certificate extensions are just additional information in the certificate, i.e. "extending" on the information which has to be provided at minimum. If you need these extensions you have to use X.509v3, without extensions you can use X.509v1. Typical extensions are usage restrictions, subject alternative names or links to CRL download and the OCSP resolver.
A certificate can contain multiple extensions and this is actually the common case. The server can differ between the various extensions because each has a type id which is contained in the X.509 file. For more detailed information about the variety of extensions which exist see Redhat: B.3. Standard X.509 v3 Certificate Extension Reference.
Certificate extensions have nothing to do with file name extension, hair extensions, loan extensions or any other kind of extensions.