The idea is, some offices and colleges block Webmail sites. You’ll find out soon enough. Even otherwise, it doesn’t “look good” if you’re often seen with a Gmail window open (and since Gmail integrates a chat facility, you might be tempted to visit www.gmail.com quite often). But remember that Gmail (for one) offers you the facility of downloading your mail via POP3 and/or IMAP to your mail program: in Gmail, just click on Settings, then go to the “Forwarding and POP3/IMAP” tab.
The choice is getting a bit hazy. For one, connection speeds are improving, so much of the virtue of IMAP is getting eroded. Second, many Webmail sites (notably the new Beta of Yahoo! Mail) are giving you the look and feel of a mail program. Third, you’re more likely than ever to see Webmail interfaces for, say, your office mail, or your domain mail. And then, you have the fact that, for example, Gmail as mentioned above, gives you free POP3 and IMAP mail (God alone knows why they do it; you don’t see any Google ads in your mail program when you use POP3 or IMAP for your Gmail).