Crystal Gems are objects displayed in the player's trophy room. When the player has created a crystal gem for a certain area, henchmen can no longer steal your coins whilst in that area. The colour of the gem/shards also corresponds to the colour of the area's portal and henchmen (e.g. purple for Funkeystown).
How to Obtain Edit
Crystal Gems are made up of gem shards. These gem shards are objects obtained by reaching a certain cumulative score in any game in the four main worlds (Funkeystown, Magma Gorge, Laputa Station and Kelpy Basin). These shards are displayed in the Trophy Room in the player's crib. When four of these Gem Shards are collected, they form a Crystal Gem.
In the 'Funkeystown Gem' cutscene, Mayor Sayso says that the energy released by the repaired gem causes the Henchmen's programming to go haywire.