An airdrop is a way to distribute coins. End users can generally get coins for free or in exchange for a small task, such as subscribing to a newsletter, sending a tweet or inviting other people via a personal affiliate link.
Cold storage refers to storing cryptocurrency on a place where the private key cannot be accessed via the internet. This can be done on a hardware wallet, paper wallet or software wallet in an offline environment.
Bounties are simple tasks of jobs by the team behind a coin. These can be as simple as joining a Telegram channel or by (re)tweeting. It could also be a bit more difficult like a translation job for example. The participants receive rewards in the form of coins in exchange for completing these bounties.
The block reward is the payment that is offered to the node that is securing the blockchain. In the case of Bitcoin, which is has a Proof-of-Work consensus algorithm, these would be the miners. The payment is in the form of the native cryptocurrency of that blockchain. The amount is a predetermined reward per block, but often that is supplemented with the fees that are paid for the transactions that block contains. For Bitcoin the current block rewards are cut in half every four years. This is called the ‘halvening’.
A block explorer is an online service to track blockchain transactions. It usually is a website where you can see all the new blocks that are being created. You can also search for transactions and wallet addresses. The best-known block explorers are blockchain.info for Bitcoin and etherscan.io for Ethereum.