Ether is the native token of the Ethereum network and is used to pay fees for state changes to the blockchain including creating and interacting with smart contracts. It can be easily transferred from one account to another with no jurisdiction restrictions and is traded on many online exchanges mainly against bitcoin, USD, EUR and KRW. Ether was first created in a crowdfund to raise funds for development by exchanging for bitcoin.source
Other than price, the trading volume can also be measured to show the amount of trading activity and liquidity involved in the ether market.source
Ether is also created constantly by a process called mining where fees plus a block reward is given to anyone or anything that is able to verify valid transactions and add them to the blockchain through proof of work. This adds about 5 ether to the total supply roughly every 14 seconds. Therefore the total value is also relevant when looking at the price of each ether.source
As more miners participate to verify blocks, blocks can be verified much faster than 14 seconds and more batches of 5 ether will be created. To counteract this, a difficulty is set for miners and can be adjusted dynamically to ensure a more constant block time of around 14 seconds and control the rate of ether creation. The difficulty of the network can be used to measure the amount of resources dedicated to mining ether.source
Coinbase is one of the main exchanges that users can sign up, transfer in money and use it to buy ether. Their number of users can give an indication of the amount of new interest in Ethereum.source
Google Trends gives an indication of the amount of internet search interest on Ethereum, which can include new people wanting to know more about it to developers searching for smart contracts solutions to entrepreneurs trying to build next generation applications.source
All state changes in Ethereum such as ether transfer and interactions with smart contracts are done through transactions. Transactions are all signed cryptographically and stored. The number of transactions can give a rough indication on the amount of activity and utilization of the network.source
The Ethereum subreddit is the main place where public discussions happen. Topics can range from new comers asking for help, project/event announcements/discussions, encouraging each other and friendly banter with developers and other Ethereum lovers/haters.source
geth is currently the most popular Ethereum client. It is open source and implemented in golang. It is an Ethereum node and can be used to communicate with other Ethereum nodes, verify transactions, broadcast/relay transactions, interact with smart contracts etc. The Github stars can indicate the amount of interest Github users have in the more technical aspect of Ethereum.
MetaMask is a chrome extension that enables users to interact with applications built on Ethereum from the web browser without the hassle of running a client like geth. This allows developers to leverage on existing web development technologies to build decentralized applications. The number of active users is a good indication of Ethereum users and usage of Ethereum applications.source
web3.js is one of the libraries built for more abstract communication with Ethereum nodes. It enables creating and signing of transactions, querying smart contracts etc. The amount of downloads is a good indication of the amount of developers building and exploring Ethereum.source
solc-js is one of the compilers for Solidity, one of the smart contract language for Ethereum. It compiles high level language into machine code for execution in the Ethereum virtual machine. The amount of downloads is a good indication of the amount of developers building smart contracts.