What is the difference between IQueryable<T> and IEnumerable<T>?
The primary difference is that the LINQ operators for IQueryable<T> take Expression objects instead of delegates, meaning the custom query logic it receives, e.g., a predicate or value selector, is in the form of an expression tree instead of a delegate to a method.
IEnumerable<T> is great for working with sequences that are iterated in-memory, but IQueryable<T> allows for out-of memory things like a remote data source, such as a database or web service.
Where the execution of a query is going to be performed "in process," typically all that's required is the code (as code) to execute each part of the query. Where the execution will be performed out-of-process, the logic of the query has to be represented in data such that the LINQ provider can convert it into the appropriate form for the out-of-memory execution - whether that's an LDAP query, SQL or whatever.
More in C# 3.0 and LINQ.
First of all, IQueryable<T> extends the IEnumerable<T> interface, so anything you can do with a "plain" IEnumerable<T>, you can also do with an IQueryable<T>.
IEnumerable<T> just has a GetEnumerator() method that returns an Enumerator<T> for which you can call its MoveNext() method to iterate through a sequence of T.
What IQueryable<T> has that IEnumerable<T> doesn't are two properties in particular—one that points to a query provider (e.g., a LINQ to SQL provider) and another one pointing to a query expression representing the IQueryable<T> object as a runtime-traversable expression that can be understood by the given query provider (for the most part, you can't give a LINQ to SQL expression to a LINQ to Entities provider without an exception being thrown).
The expression can simply be a constant expression of the object itself or a more complex tree of a composed set of query operators and operands. The query provider's IQueryProvider.Execute() or IQueryProvider.CreateQuery() methods are called with an Expression passed to it, and then either a query result or another IQueryable is returned, respectively.