Dropping a column that is not referenced by any other object lets the storage engine simply mark the column definition as no longer present. Deleting the meta-data invalidates the procedure cache. Any query that subsequently references the affected table will result in the plan for that query be recompiled. The recompile operation can only return columns that currently exist in the table. As a result, the storage engine skips the bytes stored in each page for the dropped column, as if the column no longer exists.
This has some nice benefits in practice around minimizing deployment-releated downtime.