There are three implementations of AsEnumerable.
DataTableExtensions.AsEnumerable
Extends a DataTable to give it an IEnumerable interface so you can use Linq against the DataTable.
Enumerable.AsEnumerable<TSource> and ParallelEnumerable.AsEnumerable<TSource>
The AsEnumerable<TSource>(IEnumerable<TSource>) method has no effect
  other than to change the compile-time type of source from a type that
  implements IEnumerable<T> to IEnumerable<T> itself.
AsEnumerable<TSource>(IEnumerable<TSource>) can be used to choose
  between query implementations when a sequence implements
  IEnumerable<T> but also has a different set of public query methods
  available. For example, given a generic class Table that implements
  IEnumerable<T> and has its own methods such as Where, Select, and
  SelectMany, a call to Where would invoke the public Where method of
  Table. A Table type that represents a database table could have a
  Where method that takes the predicate argument as an expression tree
  and converts the tree to SQL for remote execution. If remote execution
  is not desired, for example because the predicate invokes a local
  method, the AsEnumerable<TSource> method can be used to hide the
  custom methods and instead make the standard query operators
  available.
In other words.
If I have an
IQueryable<X> sequence = ...;
from a LinqProvider, like Entity Framework, and I do,
sequence.Where(x => SomeUnusualPredicate(x));
that query will be composed and run on the server. This will fail at runtime because the EntityFramework doesn't know how to convert SomeUnusualPredicate into SQL.
If I want that to run the statement with Linq to Objects instead,  I do,
sequence.AsEnumerable().Where(x => SomeUnusualPredicate(x));
now the server will return all the data and the Enumerable.Where from Linq to Objects will be used instead of the Query Provider's implementation.
It won't matter that Entity Framework doesn't know how to interpret SomeUnusualPredicate,  my function will be used directly. (However, this may be an inefficient approach since all rows will be returned from the server.)