What's Cron Service?
Permanently working M2E Pro automatic synchronization is provided by M2E Pro Cron Service. It is a background mechanism for a constant script running. No particular settings for Cron Sevice are required. Yet, an important condition is that Magento server must accept the incoming calls from M2E Pro Cron server. For that, IP addresses 22.214.171.124 and 126.96.36.199 must be allowed in your firewall settings.
You can see the Cron Service work status under eBay/Amazon/Walmart > Help Center > Cron Info in your M2E Pro Module.
Why an automatic synchronization is required for eBay/Amazon/Walmart integration?
When the requests are submitted to Channel servers, the responses are not received immediately. This is due to Channel systems peculiarity. For example, to get a response from Amazon API, M2E Pro needs to constantly check if the requests are processed. That's why Channel API uses a queue system: all sent requests are queued and processed on a “first-come, first-served" basis.
So, permanently working automatic synchronization is required to perform the tasks on eBay/Amazon/Walmart (e.g., quantity and price updating, orders importing/creation, etc.).