So Etherwallet (https://github.com/kvhnuke/etherwallet) is a wallet which runs on the browser, how is it possible to send transactions without download the entire copy of the blockchain ? or Etherwallet have some background service to validate the transactions ?
MyEtherWallet.com has a node running on their backend. You sign the transaction in your browser (to address, amount, signed with your private key) and the node broadcasts it. This ensures the private key never leaves your browser - just the already signed transaction.
It's different than you running a local node with an account in it that you unlock to sign and send transactions. It's basically the same thing that you can do via this page on Etherscan, except that MyEtherWallet.com has the ability to generate the signed transaction for you in the same place.
There is a major difference between MIST (Ethereum's own Wallet) and any third party wallets (MyEthereumWallet.com). MIST is both a node and a wallet, which means all the blocks has to be synced before a transaction become valid. Whereas any other wallets (either browser based or mobile apps) have a server-side implementation of the node. Each wallet is an account and your wallet company node does transactions. It's wise to choose reputed companies as this server-side implementation isn't open-source and can't gaurentee what happens there.