Anonymous data is personal data from which all identifiers have been removed so that it is no longer possible to identify the person in question.
It is not always possible to anonymise data just by removing names, addresses and other direct personal identifiers. Data on the basis of which an individual can be indirectly identified must also be removed. This data can include information on a rare disease or on receiving a certain social welfare service.
Therefore, an individual cannot be identified even indirectly from anonymous data. As long as an individual can be identified even indirectly from data or the data can be changed back to the form in which it contained identifiers, the data in question is personal data. For example, genome data is data that cannot in practice be anonymised.
A data protection working party (WP29) in the European Union has given a statement related to methods for anonymisation.  It lists the aspects that must be taken into consideration in anonymisation.