I was not familiar with the term of "anecdote" in english. According to the wikipedia, anecdote is a some sort of short story with some point in it. Although in Russian language, for example, anecdote does not necessarily have to convey some wise point, it should be just funny. I quite confused about this term. So could you guys explain what is a purpose of anecdotes and where they are used ?
In British English, an anecdote needn't contain a point, but can be used to illustrate a point. For instance, you might tell an anecdote if it describes a specific example of a general trend or phenomenon you are talking about.
In that usage, it is being used as an informal type of "evidence". An anecdote is usually understood to be about an experience that you've had yourself -- as opposed to, for example, an urban myth ("my friend's friend said..."), or a conclusion drawn from a scientific study. Therefore, if an anecdote is used as "evidence" to make a point, you expect the person telling it to be truthful; but your conclusion is "that thing happened to that person", rather than "it happened to them, so it must be true for everyone".
By extension, if someone said "there is anecdotal evidence that wheat can cause stomach ache", they'd mean that members of the public have reported getting stomach ache after eating wheat (perhaps on social media, or in forums for people who often get stomach ache) -- but that there hasn't been a thorough science-lead study of the alleged relationship between wheat & ache. The phrase does imply that, because a lot of people have made the claim, there might be some truth in it, but also implies that this "evidence" must be treated with caution.
However, anecdotes don't have to make points. We also value them if they're funny, in which case they're told just because they're entertaining!