ONVIF’s main purpose is to provide and promote standardized interfaces for effective interoperability of IP-based physical security products. It allows for cameras to natively integrate regardless of manufacturer. Many modern surveillance camera companies comprise and adhere to the stipulations set out by ONVIF.
Being ONVIF conforming doesn't automatically mean that all manufacturers’ cameras will always be compatible. Many started supporting ONVIF at different times, so it’s not uncommon to come across a camera a manufacturer made before their products were ONVIF compatible.
If you’re wondering if your non-AvertX/3rd party camera is ONVIF compatible, check out the Conformant Products page at the ONVIF website. They have a list of products that are ONVIF compatible broken down by type, manufacturer, etc.... Not all may be listed, but it's a great place to reference if the information is not available through a 3rd party manufacturer's source.