Claiming is the process of publishing a domain onto the blockchain via your cryptocurrency wallet to gain full custody of the domain. This means that nobody else has control over it except for the rightful owner. This is what makes them decentralized, uncensorable, and therefore "unstoppable". Once claimed, neither Unstoppable Domains nor any other entity is able to make changes to the domain or take it back from you.
Note: Remember, the power of "true ownership" means having greater responsibility. Once you claim the domain to a cryptocurrency wallet, be sure to make a backup of the wallet's recovery phrase/seed words in case you lose access. Unstoppable Domains WILL NOT be able to recover your wallet for you.
To find out how to claim, please click here.