As mrvijayakumar touched on briefly, it is where you access an FTP server that doesn't require a username or password, or has a default set of credentials to login to. They are sometimes called Public FTP Servers for this reason, because anyone can use them without requiring explicit details.
It should be pointed out however that they aren't anonymous in every aspect, when you access the server it is likely that details shall be logged such as an IP, what time it was accessed, and what modifications (such as adding or retrieving files) have been made.
If that line of thinking was adopted by these forums then there would be 0.00 discussions taking place here.
For example, and this is an overly simplified example, you want to know how to spell the word 'gnome'. You ask someone how to spell the word and they abruptly tell you to get a dictionary. So, you go and get a dictionary and because you didn't know that the word 'gnome' begins with a silent 'g' you spend a lot of time looking up all the words beginning with the letter 'n'. You simply wouldn't find your answer, would you?
Another good reason for asking questions in a forum setting is that you will be helped with an answer in context with your problem. For example, if a person says they have a projector with the model number ABC123 and wanted to know the best way to connect it to a Tablet with the model number ZYX321, then researching this via Google may be complicated for some people. But, in a discussion forum like this it would not take someone with some technical expecting to do a few quick checks on specs and then provide an answer or some options.
So, Mr. Rik from RCE, please check this link for more info:
People that ask questions like this are usually doing it for homework from school or projects for university. I don't know about you but I have better things to spend my time on, like people that have problems that need help.