A smart contract is easier to grasp with a plain example. Imagine a vending machine. You put in the right amount, you press the button, and the machine releases your item. No cashier, no negotiation. The rules are built into the machine, and it follows them every time.
In traditional banking, the bank holds your money and you prove who you are to access it. Crypto works differently, and private keys are the reason why.
Bitcoin is where the entire crypto market began. It launched in 2009 as the first working example of digital money that doesn't need a bank or a government standing behind it. Everything that came afterward is, in some way, a response to it.
Every cryptocurrency you've heard of runs on the same underlying invention: the blockchain. Before you look at any individual coin, this is the concept worth understanding first, because everything else builds on top of it.