First let me say, there is some truth in both answers from Tim X and David Wachtvogel. I'd still like to correct some of the statements of both of them.
First, the impact
Usually on a POP3 server, the messages are deleted after you download them. If a hacker would get your password he cannot get past messages. This is sometimes configurable, but by default it should still delete messages when your clients downloads them.
IMAP on the other side is designed to keep your messages on the email server, so you can download it from multiple clients, or re-download it, if your local client is lost (for example you deleted your email account).
The email provider can most often read your email password in plaintext regardless of how you protect yourself, so you should always use a dedicated password (only used for ONE provider).
In essence there are three things that could protect your email and one of them would protect your password.
Let's start from the bottom.
1. The storage
If your email is hosted on a 'shared server' it is usually accessible without any hurdles by whoever has access to that server. This includes a technician of your hosting provider, who has access to the physical device, a hacker, who has access to your operating system as well as any user that has access to your credentials. As mentioned above, in the case of POP3 this is usually limited to "new" mail, but in the case of IMAP, it is not limited at all.
Usually you cannot do anything against this type of attack, but also usually big providers can be trusted to not look into your emails, as long as no government agency is involved. Some exception apply as some providers (google, microsoft, possibly others) do automated analysis on the contents of your email to present ads to you. This can only be prevented by point 3.
2. The transport
The second part to protect is if you sent an email to your provider or receive an email from them. This usually uses TLS/SSL protections (the same as with secure websites, starting with 'https://'). An attacker cannot read what is inside the emails. An attacker can also not read what is inside your authentication. This is the only way to keep people from stealing your password. Still, the Email-provider could log your password in most cases. This will keep your emails and your password secure from 3rd party people listening in on your connection.
If the sender and recipient of the message are on the same provider and you would trust the provider, it would be considered relatively secure. This most often applies to company mail servers, for sending emails between your colleagues.
As Tim X mentioned, the warning may be because your mail provider may not support encryption, your client may not support (that) encryption OR
the certificate used by your mail provider may not be trusted by your client. This may sound dangerous, but actually in most of the cases it is not. If the certificate is issued by an authority your client does not trust, it would still be secure, as long as the certificate is correct. There are multiple ways to confirm it, but in general it is pretty rare that somebody would intercept your connection, just as you are setting it up for the first time.
3. The Encryption
If you really want to be sure that only the desired recipient of the message should be able to read it, you should be using any form of email encryption (and maybe signing). This way, you can be sure only one person is allowed to read your email and nothing in between can disturb this. You might need some additional program or plug-in, though. There's currently S/MIME and PGP available and what to use primarily depends on your peers and your needs. Both should deliver a sufficient level of cryptography.
The biggest drawback: Both parties need to use the same solution. In advance. In contrast to what Tim X said, the people you send to must not have your public key, but you will have to have THEIR public key at the time you write the message. You will encrypt it with their public key, so they can only decrypt it with THEIR secret private key. This is called end-to-end encryption and is the most secure of it all.
4. Bonus
If you do not use end-to-end encryption as explained in point 3, your email is only secured as you send it to your own mail provider. If the recipient is on another provider (say, you send an email from yahoo to hotmail/bing), there is a big possibility that the transfer in-between the two providers is unencrypted. In this example, yahoo will receive your email encrypted from you, maybe store it safely, but then open a channel to hotmail and forward the unencrypted text. The only chance to mitigate against this is to use end-to-end encryption as in point 3.
It should be noted though, that more and more providers today start to use encrypted connections even between servers, but this is not yet mandatory.
Conclusion
If you want to send birthday greetings to your grandma: Use at least point 2, so your password is not stolen. This especially applies if you sometimes send emails from public hotspots. The Wifi is not encrypted and if your email connection is not, everybody can read your password and your email.
If you want to send confidential data to a friend: Use at least points 2 and maybe 4 to have very few attack vectors.
If you want to protect against the government spying on you, use at least point 2 and 4 (or 3 alternatively).
If you're paranoid use point 2, 3 and 4
To mitigate the impact of 1, either choose a good hosting provider or host yourself on a root server with hard disk encryption enabled.
