Phishing is the new designation or electronic version of a swindle.
If you get an email from paypal saying that they are doing a security check and to log in... that is someone phishing for your paypal login. What will happen is you will be directed to a look-alike site (not paypal) and when you enter your information you just got swindled, because now someone else has it and can use it to pay for their orders. Usually this kind of email is sent to "undisclosed recipients" which PayPal would never do (neither would ebay). If you get an email to "undisclosed recipients" it's someone phishing for information 99% of the time.
You can get a pop-up while surfing that looks like a legitimate warning "you are infected, click here to remove the infection" (this same warning can come via email). When you click to have it removed, you just installed the infection that you never had. Again, swindled. Now the one phishing will legitimately say you are infected and that you will need to buy their product to have the infection removed. This is known as "ransomware"... but it still started with phishing and being swindled. The only legitimate warning of this nature will come from your anti-virus or anti-spyware software... you should know the name of it and only heed warnings from that or those products.
Sometimes your bank (or a bank you never heard of before) will say you need to click here and enter your login info... doing so will give your bank info to someone else because the email was a fake. If your bank really has a notice for you, it will present itself the next time you log in normally to your account. They don't send out emails asking you to log in. They might send an email telling you what will happen the next time you do log in, but that's not the same as providing a log-in link in the email. If you didn't go to your banks website yourself (not via email) then don't enter your info!
Then there's the ones that really snooker the kids. They go to download music, or a ring tone, or a movie, or a game, or whatever... usually that's fine. But some sites will pop up a window with an agreement you have to agree to in order to get the freebie. Problem is, no one reads this thing. It usually will state that by agreeing you will also be downloading a program that keeps tabs on where you go on the internet, and it will pop up ads from then on that relates to what you do on the internet. This is called adware or spyware. One or two of them isn't so bad... but when you end up (over time) with dozens or hundreds, it can slow your computer down to an absolute crawl.
I'd say 80% of the repairs I do are just in getting rid of these things. Some of them are next to impossible to find and remove... making it that much more difficult.
Another phishing move is someone from nigeria (or even a made up country) saying they want to give you money... just email them. What they will do is have you start a bank account with your own money to open it, then ask you for the routing number and account number to transfer their money to you... but instead will take your money and close the account. Or worse, talk you into helping them with bribes (by you sending them money) so they can free up their cash. Or any number of other scams. It's like this, no one you don't know is going to give you money, you didn't win an international lottery that you never entered (and that doesn't exist), and unless you used your favorites (or bookmarks) or typed in the URL yourself, you don't need to enter your log in information.... someone is out to take your money if you do not use some caution.
That being said, just ordering online is not nearly as risky, odds are you know the company you're dealing with and you went there because you wanted to and you plan to buy a real product. So don't stop internet banking or shopping, just use caution and don't get caught by those phishing.