Excerpt from BOL ...

Aligned index :

For aligned index ,Index is partitioned in same manner as the base table, using same partition scheme and partitioning column.

When a table and its indexes are in alignment, SQL Server can switch partitions quickly and efficiently while maintaining the partition structure of both the table and its indexes.

Non aligned Indexes :

Designing a partitioned index independently (unaligned) of the base table can be useful in the following cases:

The base table has not been partitioned.

The index key is unique and it does not contain the partitioning column of the table.

You want the base table to participate in collocated joins with more tables using different join columns.