Email comes in different flavors. How you deal with email is either with a browser (like Safari or Google Chrome) or with a dedicated email program, like (Mac) Mail or Outlook. Using a browser for email is referred to as webmail. Popular providers like Google (Gmail) or Comcast allow you to view your messages either way. In fact, virtually all email can be viewed either way, but some providers make it easy, and others more cumbersome to use webmail.
Webmail is all you need, and many of my clients using Gmail or Comcast read and manage their email only with a browser. Others find webmail clumsy and just don't like the interface. Of course you can't access webmail without an internet connection.
What Is an Email Server?
(or, How Does Email Get To Me?)
When you send an email it lands on a big computer somewhere, in a spot reserved for it by the recipient's email address. The storage devices that these computers run are called servers (actually email servers, as there are also other kinds of servers). Sometimes emails stay on the server until you take them off (IMAP), and sometimes they just hang out there until they are delivered (POP). Webmail is a way of seeing and interfacing with what is on the server, sort of directly.
Using An Email Client
The program on your computer (or device) used for email is called an email client. Often, email can be set up automatically with just an address (user name) and a password. The email client, just by seeing the address itself, can understand what protocols to use and set things up for you.
They do this by choosing from two main options: IMAP and POP. Mostly the program will set up your email with IMAP and just not tell you. Some will ask you which you prefer, while others use POP.
POP is a slightly older protocol which made a lot of sense when we had just one computer, no laptop, and no smartphones or tablets. With POP, your mail just gets dumped onto your computer. It usually is deleted from the server after delivery to the email client, either immediately, or after a certain amount of time (usually a week by default). If you have a desktop and a laptop, or a computer and a smartphone, each one of those gets mail from the server. The server, aside from being told when it can delete delivered messages, doesn't know what is done with those messages on each device.
The results can be astonishing, with one computer showing 1200 unread emails in the inbox, and other showing 125 unread emails – and this is the same email account, the same email address. Other possible problems include some emails appearing on one device and not another. This can result from the "delete from server" delay being set to different amounts of time on two devices, or simply by not going online and getting mail often enough, allowing the messages to be deleted before they can be delivered to a second (or third or fourth) device.
IMAP is more like webmail in that it shows you what is on the server in real time. Any changes you make (delete, reply, forward, move) are reflected on all devices, as soon as those devices are connected to the internet. Since all your inboxes stay in sync, you see the same amount of unread messages on your iPhone and your MacBook Air. Also, the emails that you have filed into folders can live on the server, meaning all your devices will have access to them.
I want IMAP but my ISP doesn't offer it.
Except in rare cases, POP email is a problem, not because of the technology not working, but because it doesn't make sense for the way we access email. But what can you do if you have an email address, like Earthlink, that does not support IMAP? What I recommend is forwarding all that email to a new address. I usually use Gmail. You can set an account up for free, and it will even pretend to be your old address if you ask it to.