How Email Works
Email is actually quite synonymous with postal mail. All messages have a source, destination, and body and get routed in a similar fashion.
The whole process kicks off when the computer builds an email message. This message is then sent up to your internet service providers (ISP) mail server (think of it as taking the message to your corner postal box). The ISP then looks at the destination of the message finds the address of the server email is supposed to be delivered to. Once the address is found the ISP mail server talks to the destination mail server which accepts the message and puts it into the recipients mailbox. The technical term for this process is often referred to as SMTP (Simple Mail Transfer Protocol).
For the client to get the message you sent them they will need to log into their ISPs server (the one we delivered the message to) and download their new messages. This is often done over a protocol called POP3 (Post Office Protocol version 3) or the lesser used IMAP (Internet Message Access Protocol).
Email is quite a simple and reliable system. If the destination mail server is down your ISP server will continue to try and deliver the message for hours or sometimes days. Many servers will accept mail even if there is a problem with itself and hold it in a queue until the problem is resolved. With all the built-in redundancies it is quite hard for an email message to just randomly get lost.