Domain names are used by your web browser to help internet users connect to websites and operate internet services like email. .org is one of the longest stablished and most trusted top-level domains (TLD) worldwide. It is used especially by non-governmental organizations or not-for-profit organizations to indicate scale, trust or when aiming at a global audience. If you are a non-profit looking to promote yourself to a US or international audience in a less commercial manner, using .org is a good choice.
You can register a .org domain name by searching for it using the availability checker on this page. Once your ideal domain shows as available, you can register it (along with other domains if you want).
.org domains can be registered for annual terms from 1 to 10 years. Once you hold a .org domain name, you can renew it by adding additional years it any time before it expires as long as the total period is less than 10 years.