If you have used official Ethereum Wallet(Mist) from Ethereum.org, you'll know how slow it is to synchronize. It took more than 24 hours for me. It downloads and verifies every block in the blockchain which is over 30 GB. And it's growing rapidly, so you should have some disk space available for the blockchain storage. If you are not running your wallet(or Geth which is the backend that take cares of blockchain in the background), you have to wait for the wallet to catch up with the current state of the blockchain when you want to use your wallet.
Although downloading and verifying every block in the blockchain is a good thing for security, user experience is not so good, especially if you are running it for the first time. I guess thats why myetherwallet.com is so popular. Although you are not running a node, you do have direct access to your private keys. You can also change backend node you connect to, so if one goes down you can connect to another provider. I use mytherwallet.com because I can use it with my hardware wallet. And official Ethereum wallet was to slow, and I didn't have much space on my laptop.
You can now synchronize faster with the official Ethereum wallet. Synchronization took less than an hour, and it stored 340MB of data including ethash and lightchaindata.
Here is how to synchronize faster:
Download recent version of Geth from https://geth.ethereum.org/downloads/ and unarchive.
Run geth from Terminal with arguments --syncmode=light
geth-1.8.1 --syncmode=light
Run Ethereum Wallet. It should connect to the running geth and should be in full sync within an hour (depends on your connection speed)
