Layman’s definition : Ethereum is a new version of the internet used for reliable, secure apps.
Technical definition: Ethereum is an opensource, decentralized platform that runs applications exactly as programmed without any possibility of downtime, censorship, third party interference or fraud (These apps are commonly referred to as smart contracts) .
Explanation of technical definition
opensource means that the software is not owned by anyone or any company. It is free to use and modify!
decentralized means that the processing/storage/running of the ethereum software is shared between many computers which are not owned by one group. It has been described as a world computer as the software can run on any willing users computer, regardless of location. In return for running this software the computer it is awarded some a financial reward.
downtime is when a service is unavailable, often commonly due to a surge in traffic or a hack. Ethereum is resistant to attack by hackers and cannot be shut down by anyone because it is operates as a decenteralized system.
censorship is when content is selectively blocked. This could be because someone doesn’t agree with the content or some third party interferes or threatens the person running the software. It is not possible to censor secretly in ethereum because any censorship rules would have to be written in the running code which is clearly visible to all users.
fraud in this context is deliberate deception to secure unfair or unlawful gain. This is not possible in ethereum as the code that is running can be inspected and the account that will take payments is clearly visible to all users. That said, the identity of an account holder can only be found if they choose to publicly declare their account address.