Push eg. completed orders from WooCommerce to your other system.
Updating the stock balances according to the received information from the other software.
Updating product and pricing data based of the information received from the other end.
Get information about the updated order statuses and inform your customers about the changes.
WooCommerce is one of the most popular eCommerce platforms in the world. It's easy to customize and connect to other systems like accounting or CRM.
We at Flashnode work closely with many WooCommerce agencies. If you're about to start eCommerce business with WooCommerce, feel free to touch base.
Based on your requirements and other systems being used, we can probably mention a couple good agencies that could help you further.