@Phoebe. The page shows your current status with each giant. If it's showing an emblem, that means you need to go to that Giant's shrine and collect the emblem you've earned.
Your favor for that Giant will reset to 0 and the amount needed to collect your next emblem from that Giant will increase by 100.
I love this so much and will heavily make use of it. But I would like to add a vote for listing the Giants in alphabetical order. It will be much easier and more understandable. Thanks!