A smart contract is a computer program or a transaction protocol respectively, which is intended to automatically execute, control or document respectively legally relevant events and actions according to the terms of a contract, of an agreement or of a negotiation.
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.
Bitcoin is a digital or virtual cryptocurrency created in 2009 that uses peer-to-peer technology to facilitate instant payments.
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.
2 Factor Authentication is a double layer security measure. Most crypto exchanges use it. In order to log in, you not only need to enter a password, but also a code that you receive from the Google authenticator for example.