When an index is reorganized what is compaction.

From https://technet.microsoft.com/en-us/library/ms189858(v=sql.110).aspx We have "Reorganizing an index uses minimal system resources. It defragments the leaf level of clustered and nonclustered indexes on tables and views by physically reordering the leaf-level pages to match the logical, left to right, order of the leaf nodes. Reorganizing also compacts the index pages. Compaction is based on the existing fill factor value" I can understand the physical re-ordering. However the compaction part confuses me. If a page space uses more space than the fill factor then surely compaction down to the fill factor value will cause a split which could affect pages at a higher level.