Action in Session API context means fetching recommendations for a specific view. For example when visitor navigates from front page to a product view you would most likely fetch recommendations related to a product. This would be considered as Action. Setting the cart contents however would not be considered as action.
It's also good to keep in mind that each Action is considered as a page view in Nosto's analytics. It's recommended to perform an action only once per route change to keep the analytics consistent and comparable to traditional "static" e-commerce stores.
Route change in the context of this documentation it means, as it stands, when the navigational route (url) of the application is changed. In traditional web sites this would be a (full) page load.