If a mailbox is offline
When an email account is offline, a lightning bolt icon 
appears at the end of the Favorites bar, just below the search field. The icon also appears next to the account’s mailboxes in the Mail sidebar. (To show the sidebar, click Mailboxes in the Favorites bar.)
Take all accounts online: Click the lightning bolt icon or choose Mailbox > Take All Accounts Online.
Take a specific account online (if you have more than one account): Click the lightning bolt icon next to the account’s mailbox, or choose Mailbox > Online Status > Take [account] Online.
If you can’t take an account online, make sure you’re connected to the Internet. If a warning icon 
appears next to the account name, click it to open Connection Doctor. Learn more about using Connection Doctor.
Some mailbox names can appear dimmed if you don’t have permission to access them, such as public mailboxes on a mail server.