Schema and cube is defined in the following way on Mondrian's documentation page—http://mondrian.pentaho.com/documentation/schema.php:
A schema defines a multi-dimensional database. It contains a logical model, consisting of cubes, hierarchies, and members, and a mapping of this model onto a physical model.
The logical model consists of the constructs used to write queries in MDX language: cubes, dimensions, hierarchies, levels, and members.
The physical model is the source of the data which is presented through the logical model.
Cube is a basic construct of Data Warehousing discussion of which is out of this book's scope as there are numerous books existing on this topic and explaining it here may not be a good idea.