Staking your hard earned Trilium to one particular planet increases the TLM rewarded to that planet during the daily Trilium allotment from the Federation. You are also rewarded tokens from that particular planet at a 1:1 ratio. These tokens can be used to partake in planetary governance as well.
It takes two days to unstake from a Planet, to prevent a whale Trilium holder from staking to a Planet just prior to Planet’s Trilium allocation being calculated, and then moving to another Planet
Staking commits some of the Trilium to a particular planet and can only be removed after a two-day waiting period. It is important that Trilium be staked to a planet, as the governance functionality of that planet cannot be awarded to the Explorers until it reaches a sustainable level, in the eyes of the Federation. Staking is recorded on the blockchain and can be viewed in real-time at the links below.
To begin staking Trilium simply click the staking button (green arrow above).
You are then brought to this screen (above) where you have a few choices. To stake your Trilium click the stake button (yellow arrow). To unstake Trilium select the unstake button (green arrow). To view other planets click the arrow to the right of the screen (purple arrow).
If you choose to ‘stake’ you are brought to this screen with several more options. You can choose to stake a particular amount of Trilium by entering the amount into the box manually (green arrow). You can also choose to stake a certain percentage of your Trilium if you choose (yellow arrow). After you make your decision, press the confirm button (blue arrow). You can also switch to the unstake screen at anytime (red arrow). The mechanics of unstaking work exactly the same as staking, with one addition, you can view your staking history (green arrow below) from this screen. Selecting the history button brings you to the history screen (second screen below) which shows your staking history.
For more information on staking and governance check out this medium post.