A hypercupe is a specific XBRL element which contains all dimensions used in a specific section of an XBRL file (this could be the statement of changes in equity for instance).
What is a dimension?
A dimension is an extra property attached to an element. For instance in the statement of changes in equity "balance at the beginning of the period" is shown with different values in different columns. Those different values all have individual properties, and those properties are called "dimension members". These members are all part of the "Components of Equity" dimension.
Dimensions in the Linkbase
In the reporting package there is something called the "definition linkbase". It is specified in the definition linkbase which dimensions are used in each individual section.
In the image below you can see that the Statement of Changes in Equity contains a hypercube with one dimension and a dimension member.