Datadog organizations allow you to separate users and data within your overall account. This is particularly useful for larger or divided companies that need to maintain separation between areas.
Generally, I recommend at least two organizations in an account. One as the payer account and one child organization. This is the same model you would see in AWS, where there is a payer/root account that manages the organization and many child accounts.
You may be tempted to split your production and non-production envrionments into separate accounts. I do not recommend this pattern at all, because it makes it much more complicated to evaluate signals across environments, and your teams may occasionally use production endpoints in non-production services and it will be harder to trace across this pathway. You can keep a separate account for testing, especially infrastructure-as-code testing, experiments, or when there are truly separate business units that do not intertwine at all.
Datadog runs many copies of itself across different clouds and regions. Each organization can be homed to a different cloud and region as appropriate. If you are a single cloud company (most are), be sure to pick the cloud and region closest to your actual running cloud infrastructure. If you are primarily an on-prem company, just choose the region closest to you. Another benefit of having a payer account and sub organizations is that you can create organizations homed to each account (as long as their data is disconnected).