Ethereum is a decentralized platform that runs smart contracts: applications that run exactly as programmed without any possibility of fraud or third party interference.
These apps run on a custom built blockchain, an enormously powerful shared global infrastructure that can move value around and represent the ownership of property. This enables developers to create markets, store registries of debts or promises, move funds in accordance with instructions given long in the past (like a will or a futures contract) and many other things that have not been invented yet, all without a middleman or counterparty risk.
The project was bootstraped via an ether presale in August 2014 by fans all around the world. It is developed by the Ethereum Foundation, a Swiss non-profit, with contributions from great minds across the globe.
On traditional server architectures, every application has to set up its own servers that run their own code in isolated silos, making sharing of data hard. If a single app is compromised or goes offline, many users and other apps are affected.
On a blockchain, anyone can set up a node that replicates the necessary data for all nodes to reach an agreement and be compensated by users and app developers. This allows user data to remain private and apps to be decentralized like the Internet was supposed to work.
A cancel transaction feature on Ethereum would enable users to cancel a transaction before it is mined onto the blockchain. This would be useful if you made a mistake when sending ETH to another address, or if you changed your mind about spending ETH on a particular purchase.
Currently, there is no way to cancel an ETH transaction once it has been broadcasted to the network. The transaction will eventually be mined onto the blockchain regardless of whether or not you still want it to go through.
If you are interested in learning more about how Ethereum works, I recommend reading the whitepaper or checking out one of the many resources available online.