King of Avalon almost always has one or two seasonal events being active. At this time Merlin's Experiment Event is one of them. This guide explains how the event works.
During the duration of the event you get a chance of receiving Glass Shards items by harvesting your resource buildings and by gathering resources on the world map. When you go to the Merlin's Experiment Event in the Event Center, you can, via the Get Rewards button, exchange the Glass Shards for various goodies.
Note: For those already playing the game for a while, this event is very similar to the Valentine's Day Event, with the Chocolates being replaced by Glass Shards, and you can also acquire them via Resource Gathering, besides Harvesting.
It is just doing the things you normally do likely anyway, which is to harvest your Resource Buildings and to Gather Resources on the map.
Getting the rewards via the Event Center works a bit in a similar way as the Market Place. There are six random options to exchange one or more Glass Shards for rewards.
Whenever you accept one of the deals a new one appears.
You can auto-refresh for free three times, and afterwards you pay an increasing amount of Glass Shards for refreshing, 5, 10, 15, 20, 50. Remaining changes will cost 50.
There is a cooldown timer of 24 hours that refreshes the board and gives you new free refreshes.
There is lots of interesting stuff on offer, but you might decide to wait for special offers such as Purple Scroll Fragment for 167 Glass Shards.
I hope this helps with understanding how this even works and which offers to claim with your Glass Shards.