Firstly, it is important to understand that the "started checkout" trigger is activated when a subscriber begins the checkout process on your website. This trigger can then be used to initiate a flow in Klaviyo that sends targeted messages to the subscriber based on their behavior.

One possible explanation for the "started checkout zero times since starting this flow" filter is that it is meant to exclude subscribers who have already started the checkout process before entering the flow. In other words, the filter ensures that only subscribers who have not previously started the checkout process are included in the flow.

If you were to leave out this filter, it is possible that subscribers who have already started the checkout process before entering the flow would receive messages that are not relevant to them. For example, they might receive messages encouraging them to start the checkout process, even though they have already done so.

As for the "placed order zero times since starting this flow" filter, it is possible that this filter would remove subscribers from the flow if they make a purchase at any point during the flow. This is because the filter is looking for subscribers who have not yet placed an order since entering the flow.

@double d, yes what Tonio said. It stops loops where someone starts a checkout and then starts another one before they finish the flow. The placed order filter also kicks them out of the flow if they complete the purchase. 

Both of these would create a negative experience if they were not there.