Variable interest entity is an accounting term (also known as Special purpose entities). In simple terms, when a company deals with another party (e.g sale transaction) and that the said transaction is qualified per IFRS (accounting standards) to be a variable interest entity, then at the consolidation level (when company issues financial statements), they need to account for the variable interest entity (i.e. account for the entity’s as if it was within the company).
E.g. if A) company X buys coal from a third mining company called Y, B) X owns the majority and owns voting shares of Y, C) X is the sole buyer of coal extracted from Y and so on, it is as if Y is qualified as a variable interest entity .
In conclusion X needs to consolidate in it’s F/S Y (only to the extent of the ownership in Y).
Hope did not confuse you too much.