Difference Between Select and SelectMany

SelectMany flattens queries that return lists of lists. For example

public class PhoneNumber
{
    public string Number { get; set; }
}

public class Person
{
    public IEnumerable<PhoneNumber> PhoneNumbers { get; set; }
    public string Name { get; set; }
}

IEnumerable<Person> people = new List<Person>();

// Select gets a list of lists of phone numbers
IEnumerable<IEnumerable<PhoneNumber>> phoneLists = people.Select(p => p.PhoneNumbers);

// SelectMany flattens it to just a list of phone numbers.
IEnumerable<PhoneNumber> phoneNumbers = people.SelectMany(p => p.PhoneNumbers);

// And to include data from the parent in the result: 
// pass an expression to the second parameter (resultSelector) in the overload:
var directory = people
   .SelectMany(p => p.PhoneNumbers,
               (parent, child) => new { parent.Name, child.Number });

Live Demo on .NET Fiddle

Select many is like cross join operation in SQL where it takes the cross product.
For example if we have

Set A={a,b,c}
Set B={x,y}

Select many can be used to get the following set

{ (x,a) , (x,b) , (x,c) , (y,a) , (y,b) , (y,c) }

Note that here we take the all the possible combinations that can be made from the elements of set A and set B.

Here is a LINQ example you can try

List<string> animals = new List<string>() { "cat", "dog", "donkey" };
List<int> number = new List<int>() { 10, 20 };

var mix = number.SelectMany(num => animals, (n, a) => new { n, a });

the mix will have following elements in flat structure like

{(10,cat), (10,dog), (10,donkey), (20,cat), (20,dog), (20,donkey)}

var players = db.SoccerTeams.Where(c => c.Country == "Spain")
                            .SelectMany(c => c.players);

foreach(var player in players)
{
    Console.WriteLine(player.LastName);
}

1. De Gea
2. Alba
3. Costa
4. Villa
5. Busquets

...