The original announcement of this feature can be found here.
A small checkbox next to the X on each of your planet, starship, and starbase interface panes and also a button in the navigation which toggles between "all" and "idle" comprise the Mark Ready functionality. This is a tool to help organize your empire and turn play and reduce the time spent going through those ships, planets, and starbases that you've already managed.
As you play your turn you can choose to check off the planets, ships, and starbases you have finished giving orders to. As you check them off they will no longer be included in your idle list. So, if you have 50 planets then normally your navigation bar says Planet x of 50. But if you show only idle planets and you have marked 3 of your planets as ready then the navigation bar will show Planet x of 47. Clicking Back or Next will only move you through the planets which have not been marked as ready. When there are no more planets you will not be able to load the idle list.
The checkbox has three modes:
The following events will wake up planets:
The following events will wake up ships:
The following events will wake up starbases:
You can toggle the ready checkbox using the hotkey: "r"