Ethereum is not the only technology with Smart Contracts, so I will split my answer in two:
- Why smart contracts?
The blockchain technology introduced with Bitcoin provides a public record of transactions that you can't change in your favor. The smart contract technology exists since before Bitcoin, and consists of contracts between two or more parts that don't need human intervention to be executed. It provides security and lower contracting costs compared to traditional contracts. Associated with the blockchain transparency, it becomes more powerful since you can keep the contract terms recorded publicly in a immutable way.
- Why Ethereum?
Ethereum is the biggest smart contract platform today. The same way Bitcoin is the strongest crypto currency because it is the first and more solid, the most prominent smart contract implementation is the Ethereum blockchain platform. A lot of big companies are using or supporting Ethereum (check the Enterprise Ethereum Alliance at:
https://entethalliance.org/) and the technology is probably going to evolve more and more.
So, why Ethereum smart contracts?
Because they represent the next Internet generation, with the decentralization of everything. With Ethereum smart contracts you won't need Uber to connect drivers and passangers, and you won't need Airbnb to connect hosts and guest, and so on.
