Anonymous survey is survey conducted by researcher / author to exclude the collection of respondent's personal / private information so that whoever respondent filled up the survey is unknown.
In order to conduct an anonymous survey, the author can:
1) out-task the survey to surveying company - author might not know who are the respondents but the author also might not know whether the survey company is conducting the survey in the right manner e.g. to use random sample instead of convenient sample
2) out-task to 3rd Party e.g. school's headmaster so that s/he can collect the data from students on behalf of the author. Again same problem as No. 1 above whereby the author might not know whether the survey is conducted in the correct manner.
3) If online survey is used, don't ask respondent to provide explicit information like email / telephone etc contact number
4) If online survey is used, configure the survey website settings to exclude the collection of online respondent's email address
5) If online survey is used, configure the survey website settings to exclude the capture of IP address of the respondent's endpoint device e.g. notebook, iPad etc.
Han Ping Fung's answer summarises well the definition of anonymous survey. Below I will try to address the other part: "Is it possible to define a poll system which guarantees anonymity ?"
The major problem with implementing a real world anonymous survey is: fraud
How do you make sure one respondent takes the survey only once?
If the system is fully anonymous (to the extent of not tracking anything about the respondent, such as no ip-adress, no e-mail or any other unique verifiable id) - then essentially you are allowing one respondent to take the survey as many times as they want, thus ending up with biased data.
If you want to fight the fraud and make sure that one person can take the survey only once, then you need some kind of tracking system to recognize that person and the fact they already took the survey.
Thus "complete anonymity" in real world is not possible. At some level or the other you have to,
either live with possibly biased data (by not tracking anything at all there by the chance of one person taking the survey multiple times), or
track the minimum required thing (such as ip-address) where by you can ensure survey results are un-biased (one person - one survey take), but compromises on anonymity
Having said that, the definition of "anonymous survey" need not be "person not identifiable" - but it could be "the decision of the person not identifable".
For example, consider polls. They can be anonymous to the extent "you can know who are all voting", but "you would not know who they voted for". So, in such cases you can track 'ip-addresses' or 'e-mail addresses' - but you cannot track the voting results (the people's choices).
Thus anonymity real definition would be upto you: Anonymous IDs vs Anonymous Choices.
Can a survey using tokens ensure anonymous responses (for an example - LimeSurvey - more at: https://manual.limesurvey.org/Tokens#Can_a_survey_using_tokens_ensure_anonymous_responses.3F)?
@Frane Urem: Such token based systems demand 'trust' at one level or the other.
For example, the website claims: "If the survey is anonymous, then no link (technically: foreign key relationship) is available between the tokens table and the responses."
They claim that there will be no link between the token and the response. User has no choice but to take their word for it ('trust' their claim and use the system). Ofcouse, in case of open systems, users may get a chace to verify the code (trusting the verification process) - but for closed source systems it is very difficult (one of the reasons why organizatios like VeriSign are becoming important).
But we have seen enough systems in the industry which claim to be anonymous (non-trackable), but turns out to be not so 'non-trackable' after all.
The main challenge here is: how to establish trust between two unknown entities in a way that does not compromise either party's interests?
One main practical impact of this is in zero knowledge proofs for smart meters in the big-data smart meter analytics industry today:
How to track user's power usage in their homes without violating their privacy?
Microsoft Research has some good publications on this subject (links attached).