Active recipes are your recipes that are currently running, and accessed by the "Active" tab in your "My recipes" page. Active recipes will have a teal dot beside the job counts on the right.
When a recipe is active, you will not be able to edit the recipe at all. You will need to stop the recipe in order to edit it. When you stop and restart a recipe, it will pick up where it had left off, hence no trigger jobs will be missed.
For example, if you had turned a recipe off today and turned it on again 3 weeks later, the recipe will begin to process trigger jobs dated today (when it was stopped) and disregard the since date (which can be of any value). For more information about Since parameter, check out this article which introduces more regarding the trigger of a recipe.