Cardano

Cardano is a blockchain platform and a crypto-coin called ADA.
It is getting created by three organizations. The IOHK, Cardano Foundation, and Emurgo.
IOHK was founded by Charles Hoskinson who was also known to be an important member of Ethereum. It is considered to be the third generation of cryptocurrencies and eliminates known problems of its predecessors.
The first generation of cryptocurrencies got started with Bitcoin. With the use of blockchain, bitcoin created a way to decentralize the financial system. That means there is no central authority needed to control financial transactions.
The second generation came with Ethereum. Unlike Bitcoin, Ethereum is not "just" a coin but a platform. That means that you are not only limited to cryptocurrencies but are also able to create decentralized applications. An example of such an application could be a supply chain management blockchain that tracks products.
Now that we know about the first and second generation lets elaborate on what the third generation has to offer.
Cardano offers high Scalability, Interoperability, and Sustainability.
Scalability: The ability to adjust from a small fraction of users to a big fraction of users without performance loss.
Interoperability: This ability describes Cardano being interoperable with other cryptocurrencies.
Sustainability: We describe a system that governs and funds itself without being dependant on third parties.

ADA

Cardano's cryptocurrency-coin

Blockchain

A Blockchain is a distributed append-only ledger/register that is unmodifiable, open to anyone, and gets managed by every participant of the consensus protocol and not by a central authority. Each participant is also in the possession of a copy of the ledger/register. A consensus protocol is to define a set of rules for the users of the blockchain.

Alternative definition: A blockchain is a distributed add only data storage with the ability that the stored data is not modifiable. There is no central authority managing the data storage but we have a set of rules to keep order. Each community member that is allowed to write something in the data storage also holds a copy of the data storage on their machine, hence the name distributed data storage.

Proof of Stake

Proof of Stake is a protocol that chooses which community member is allowed to write the next block on the blockchain. The person to write(mint) the next block is chosen by the lottery.
The validators, equivalent to the miners in Proof of Work, stake their ADA to the network. Each ADA staked to the network is equivalent to one lottery ticket.
For every block, we are conducting a lottery to determine someone to write the next block. The person that wins the lottery and writes the next block is allowed to keep all transaction fees that occurred in the corresponding block.

Proof of Work

Proof of Work is a protocol that chooses which community member is allowed to write the next block on the blockchain. In this protocol, the miners have to solve a mathematical task and the first one to finish the task correctly gets the right to write the next block.
Before writing the next block the finished task has to get verified by all the other members of the quiz. If it gets verified the winner is allowed to write the next block and gets a reward depending on which coin we are talking about.

Wallets

A wallet is as the name implies a place to store your digital currencies. When you register to exchanges, like for example Coinbase or Binance, you have an online wallet to store your currencies. You are also able to download a wallet on your local machine to store your currencies locally, which is recommended for safety reasons.