Ethereum enables developers to build and deploy decentralized applications. A decentralized application or Dapp serve some particular purpose to its users. Bitcoin, for example, is a Dapp that provides its users with a peer to peer electronic cash system that enables online Bitcoin payments. Because decentralized applications are made up of code that runs on a blockchain network, they are not controlled by any individual or central entity.
In the blockchain, bitcoins are registered to bitcoin addresses. Creating a bitcoin address requires nothing more than picking a random valid private key and computing the corresponding bitcoin address. This computation can be done in a split second. But the reverse, computing the private key of a given bitcoin address, is mathematically unfeasible. Users can tell others or make public a bitcoin address without compromising its corresponding private key. Moreover, the number of valid private keys is so vast that it is extremely unlikely someone will compute a key-pair that is already in use and has funds. The vast number of valid private keys makes it unfeasible that brute force could be used to compromise a private key. To be able to spend their bitcoins, the owner must know the corresponding private key and digitally sign the transaction. The network verifies the signature using the public key; the private key is never revealed.[7]:ch. 5

Bitcoin is a digital asset designed to work in peer-to-peer transactions as a currency.[4][141] Bitcoins have three qualities useful in a currency, according to The Economist in January 2015: they are "hard to earn, limited in supply and easy to verify."[142] Per some researchers, as of 2015, bitcoin functions more as a payment system than as a currency.[36]
Until relatively recently, building blockchain applications has required a complex background in coding, cryptography, mathematics as well as significant resources. But times have changed. Previously unimagined applications, from electronic voting & digitally recorded property assets to regulatory compliance & trading are now actively being developed and deployed faster than ever before. By providing developers with the tools to build decentralized applications, Ethereum is making all of this possible.
It takes a (global) village to raise a blockchain. The live network and the community of open source developers contribute significantly to this effort. They continuously refine and harden the Ethereum platform, helping it get faster at responding to industry demands for the value propositions it offers. These investments of time and resources speak to their faith in Ethereum governance and the value that businesses and developers see in its capabilities. – Joseph Lubin, CEO of Consensys

Vitalik Buterin picked the name Ethereum after browsing Wikipedia articles about elements and science fiction, when he found the name, noting, "I immediately realized that I liked it better than all of the other alternatives that I had seen; I suppose it was the fact that sounded nice and it had the word 'ether', referring to the hypothetical invisible medium that permeates the universe and allows light to travel."[9]

One of the most important problems that any payment network has to solve is double-spending. It is a fraudulent technique of spending the same amount twice. The traditional solution was a trusted third party - a central server - that kept records of the balances and transactions. However, this method always entailed an authority basically in control of your funds and with all your personal details on hand.
The validity of each cryptocurrency's coins is provided by a blockchain. A blockchain is a continuously growing list of records, called blocks, which are linked and secured using cryptography.[23][26] Each block typically contains a hash pointer as a link to a previous block,[26] a timestamp and transaction data.[27] By design, blockchains are inherently resistant to modification of the data. It is "an open, distributed ledger that can record transactions between two parties efficiently and in a verifiable and permanent way".[28] For use as a distributed ledger, a blockchain is typically managed by a peer-to-peer network collectively adhering to a protocol for validating new blocks. Once recorded, the data in any given block cannot be altered retroactively without the alteration of all subsequent blocks, which requires collusion of the network majority.
The receiver of the first bitcoin transaction was cypherpunk Hal Finney, who had created the first reusable proof-of-work system (RPoW) in 2004.[28] Finney downloaded the bitcoin software on its release date, and on 12 January 2009 received ten bitcoins from Nakamoto.[29][30] Other early cypherpunk supporters were creators of bitcoin predecessors: Wei Dai, creator of b-money, and Nick Szabo, creator of bit gold.[25] In 2010, the first known commercial transaction using bitcoin occurred when programmer Laszlo Hanyecz bought two Papa John's pizzas for ₿10,000.[31]