Mint, Burn, and Claim
Staking on Horizon Genesis is very simple and consists of 3 actions: Mint, Burn, and Claim.

Mint

Mint is when you create, or borrow, zUSD, a zAsset stable coin tied to the value of the US Dollar, by staking HZN as collateral. zUSD can be used to trade for other zAssets in Horizon Exchange. (Note that zUSD is pronounced zee-USD.)
Horizon Genesis - Mint Page
Minting zUSD by staking HZN is similar to the concept of taking a mortgage out on your home. For example, if you own a home, you can use the home as collateral and take out money from the bank. At this point, the bank owns part of your home. To fully own your home again, you would need to pay back the money to the bank. The minting and burning mechanism in Horizon is used for this. Minting is putting down HZN as collateral to “borrow” zUSD. You then need to burn, or “return”, the zUSD to get access to your HZN again. Therefore, the zUSD is always borrowed money, also known as debt.

Burn

Burn is when you return, or pay back, some of the borrowed zUSD during minting to balance out your C-ratio.
Horizon Genesis - Burn Page

Claim

Finally, Claim is when you claim your rewards for providing collateral to the protocol, which are distributed weekly.
Horizon Genesis - Claim Page
Note that all Staking Rewards (in HZN) from your claimed rewards are locked for one year from the date that the rewards are claimed.
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Mint
Burn
Claim