We know the costing price for upgrading certain item at certain level.
For example for upgrading Purple item from +11 to +12 costs 2.550.000 emeralds. So with the Upgrade Star with 50% (for example), you will just have to press the star button ( A new button appears on the upgrade form) and upgrade right away for 1.275.000 emeralds (without the use of gems). Meanwhile, you can perform regular upgrade with gems while having the Upgrade Star and it will not get used.
The main idea behind this star is with them the game has become much cheaper. Like here, usually you have to pay around 3 million emeralds to get 1 item to +12. So basically, if you are lucky, with a good Emerald Star with +200% you will need to purchase only 600k emeralds, then get good Upgrade/Gem luck with 50% discount and here is you get your +12 Item 5 times cheaper.